Repo re-org

notebooks/cryptography_experiments.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import os\n",
+    "\n",
+    "import hashlib\n",
+    "import nacl.signing\n",
+    "from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes\n",
+    "from cryptography.hazmat.backends import default_backend"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sign_key = nacl.signing.SigningKey.generate()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "make_action_string = lambda group, index: f'reset idx={index:08x} g={group}'.encode()\n",
+    "def generate_presig(group, index):\n",
+    "    action_string = make_action_string(group, index)\n",
+    "    sig = sign_key.sign(action_string)[:64] # cut off original message\n",
+    "    \n",
+    "    key = os.urandom(16)\n",
+    "    \n",
+    "    cipher = Cipher(algorithms.AES(key), modes.CTR(b'\\0' * 16), backend=default_backend())\n",
+    "    enc = cipher.encryptor()\n",
+    "    ciphtertext = enc.update(sig)\n",
+    "    assert len(enc.finalize()) == 0\n",
+    "    \n",
+    "    return key, ciphtertext\n",
+    "\n",
+    "presigs = { group: [ generate_presig(group, index) for index in range(64) ] for group in ['all', 'v=foo', 's=bar', 'l=somewhere'] }"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(b'\\x9f\\n\\x8e\\xc9\\x1d\\xaf*\\xac\\x9e\\x1as\\xe8\\xf8\\xe6\\xe9z',\n",
+       " b'{\\xd8\\xb4\\xaf\\xb4PK1%*`\\\\\\x8e\\x93;\\x82\\xeaF\\x99\\xe0\\xbfB\\xf1\\x9d\\xae\\x02|\\xae\\\\?\\x97\\xb3\\xa5j.Y\\x83\\xddg\\x7f\\x06\\xd2\\xa47^\\xf3\\xdd\\x08n3\\x90\\x84~\\x96,tO#\\x8e$\\xdc\\xa2\\x1a\\r')"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "presigs['all'][0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def validate_presig(group, index, key, presig, verify_key=sign_key.verify_key):\n",
+    "    \"\"\" Will raise an error for invalid signature or group/index \"\"\"\n",
+    "    action_string = make_action_string(group, index)\n",
+    "    \n",
+    "    cipher = Cipher(algorithms.AES(key), modes.CTR(b'\\0' * 16), backend=default_backend())\n",
+    "    dec = cipher.decryptor()\n",
+    "    plaintext = dec.update(presig)\n",
+    "    assert len(dec.finalize()) == 0\n",
+    "    \n",
+    "    return verify_key.verify(plaintext + action_string) == action_string"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 70,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "validate_presig('all', 0, *presigs['all'][0])"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/data/.gitignore

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+*.json
+*.bin
+*.log
+*.sqlite3

notebooks/data/dsss_experiments_res-2020-02-19 16:47:31.json

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notebooks/data/rawlog_test_a.log

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notebooks/data/rawlog_test_b.log

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notebooks/data/rawlog_test_e.log

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notebooks/dsss_experiments.ipynb

@@ -0,0 +1,946 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from matplotlib import pyplot as plt\n",
+    "import numpy as np\n",
+    "from scipy import signal as sig\n",
+    "import struct\n",
+    "import random\n",
+    "import ipywidgets\n",
+    "import itertools\n",
+    "\n",
+    "import colorednoise\n",
+    "\n",
+    "np.set_printoptions(linewidth=240)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sampling_rate = 10 # sp/s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#colorednoise.powerlaw_psd_gaussian(1, int(1e4))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# From https://github.com/mubeta06/python/blob/master/signal_processing/sp/gold.py\n",
+    "preferred_pairs = {5:[[2],[1,2,3]], 6:[[5],[1,4,5]], 7:[[4],[4,5,6]],\n",
+    "                        8:[[1,2,3,6,7],[1,2,7]], 9:[[5],[3,5,6]], \n",
+    "                        10:[[2,5,9],[3,4,6,8,9]], 11:[[9],[3,6,9]]}\n",
+    "\n",
+    "def gen_gold(seq1, seq2):\n",
+    "    print(seq1.shape, seq2.shape)\n",
+    "    gold = [seq1, seq2]\n",
+    "    for shift in range(len(seq1)):\n",
+    "        gold.append(seq1 ^ np.roll(seq2, -shift))\n",
+    "    return gold\n",
+    "\n",
+    "def gold(n):\n",
+    "    n = int(n)\n",
+    "    if not n in preferred_pairs:\n",
+    "        raise KeyError('preferred pairs for %s bits unknown' % str(n))\n",
+    "    t0, t1 = preferred_pairs[n]\n",
+    "    (seq0, _st0), (seq1, _st1) = sig.max_len_seq(n, taps=t0), sig.max_len_seq(n, taps=t1)\n",
+    "    return gen_gold(seq0, seq1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "5081f9508a894fcf810e2d9c92c24a3e",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.image.AxesImage at 0x7ff8d9616610>"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.matshow(gold(5))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def modulate(data, nbits=5):\n",
+    "    # 0, 1 -> -1, 1\n",
+    "    mask = np.array(gold(nbits))*2 - 1\n",
+    "    \n",
+    "    sel = mask[data>>1]\n",
+    "    data_lsb_centered = ((data&1)*2 - 1)\n",
+    "\n",
+    "    return (np.multiply(sel, np.tile(data_lsb_centered, (2**nbits-1, 1)).T).flatten() + 1) // 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([-1, -1, -1, -1, -1,  1,  1,  1, -1, -1,  1, -1, -1, -1,  1, -1,  1, -1,  1,  1,  1,  1, -1,  1,  1, -1,  1, -1, -1,  1,  1,  1,  1,  1,  1,  1, -1, -1, -1,  1,  1, -1,  1,  1,  1, -1,  1, -1,  1, -1, -1, -1, -1,  1, -1, -1,  1, -1,\n",
+       "        1,  1, -1, -1, -1, -1, -1, -1, -1,  1,  1, -1,  1,  1, -1, -1,  1,  1,  1,  1, -1,  1, -1, -1,  1, -1,  1, -1,  1,  1,  1, -1, -1, -1,  1,  1,  1,  1,  1,  1, -1, -1,  1, -1, -1,  1,  1, -1, -1, -1, -1,  1, -1,  1,  1, -1,  1, -1,\n",
+       "        1, -1, -1, -1,  1,  1,  1, -1,  1,  1,  1,  1,  1,  1,  1, -1, -1, -1, -1,  1, -1, -1,  1, -1, -1, -1, -1, -1,  1, -1, -1, -1,  1, -1,  1,  1,  1, -1,  1, -1, -1, -1, -1, -1, -1, -1,  1,  1,  1,  1, -1,  1,  1, -1,  1,  1,  1,  1,\n",
+       "        1, -1,  1,  1,  1, -1,  1, -1, -1, -1,  1, -1,  1,  1,  1,  1, -1,  1, -1,  1, -1,  1, -1, -1, -1, -1,  1,  1,  1,  1, -1,  1, -1,  1,  1,  1,  1, -1, -1,  1,  1,  1, -1, -1, -1, -1, -1,  1, -1,  1, -1,  1, -1,  1,  1,  1,  1, -1,\n",
+       "       -1, -1, -1,  1, -1,  1, -1, -1, -1, -1,  1,  1, -1, -1, -1,  1,  1,  1,  1, -1, -1, -1,  1,  1,  1,  1,  1, -1, -1, -1, -1, -1, -1,  1,  1, -1,  1, -1, -1,  1,  1,  1, -1,  1, -1, -1, -1, -1, -1, -1,  1,  1,  1, -1, -1, -1, -1, -1,\n",
+       "        1,  1,  1,  1,  1,  1, -1, -1,  1, -1,  1,  1, -1, -1, -1,  1, -1,  1,  1,  1,  1,  1, -1, -1,  1,  1,  1, -1,  1, -1,  1, -1, -1,  1,  1,  1, -1, -1, -1,  1, -1,  1, -1,  1, -1,  1, -1, -1,  1, -1, -1, -1, -1,  1,  1, -1, -1, -1,\n",
+       "        1, -1,  1, -1,  1,  1, -1, -1, -1,  1,  1,  1, -1,  1, -1,  1, -1,  1, -1,  1,  1, -1,  1,  1,  1, -1, -1,  1, -1,  1, -1, -1, -1, -1,  1, -1,  1, -1, -1,  1,  1,  1,  1, -1,  1,  1, -1, -1, -1,  1,  1,  1,  1, -1, -1, -1,  1,  1,\n",
+       "       -1,  1, -1,  1,  1,  1,  1, -1,  1, -1,  1,  1, -1, -1, -1, -1,  1, -1, -1,  1,  1,  1, -1, -1, -1, -1,  1,  1, -1, -1,  1, -1, -1, -1, -1,  1, -1, -1,  1,  1, -1,  1, -1, -1, -1, -1, -1,  1,  1,  1,  1, -1, -1, -1, -1,  1,  1, -1,\n",
+       "       -1,  1,  1, -1,  1,  1,  1,  1, -1,  1,  1, -1, -1,  1, -1,  1,  1,  1,  1,  1, -1, -1, -1, -1,  1,  1,  1,  1, -1, -1,  1,  1])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data = np.array(list(range(16)))\n",
+    "\n",
+    "mask = np.array(gold(5))*2 - 1\n",
+    "    \n",
+    "sel = mask[data>>1]\n",
+    "data_lsb_centered = ((data&1)*2 - 1)\n",
+    "mask.shape, data.shape, sel.shape\n",
+    "\n",
+    "#fig, ax = plt.subplots()\n",
+    "#ax.plot(\n",
+    "np.multiply(sel, np.tile(data_lsb_centered, (2**5-1, 1)).T).flatten()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def correlate(sequence, nbits=5, decimation=1, mask_filter=lambda x: x):\n",
+    "    mask = np.tile(np.array(gold(nbits))[:,:,np.newaxis]*2 - 1, (1, 1, decimation)).reshape((2**nbits + 1, (2**nbits-1) * decimation))\n",
+    "\n",
+    "    sequence -= np.mean(sequence)\n",
+    "    \n",
+    "    return np.array([np.correlate(sequence, row, mode='full') for row in mask])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n",
+      "(31,) (31,)\n",
+      "shapes (1240,) (1240,)\n",
+      "(31,) (31,)\n",
+      "mask (33, 310)\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "ec8de5680ba541938b7d1843b841c327",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.image.AxesImage at 0x7ff8d955afa0>"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "nbits = 5\n",
+    "decimation = 10\n",
+    "\n",
+    "foo = np.repeat(modulate(np.array(list(range(4))), nbits).astype(float), decimation)\n",
+    "bar = np.repeat(modulate(np.array(list(range(4))), nbits) * 2.0 - 1, decimation) * 1e-3\n",
+    "print('shapes', foo.shape, bar.shape)\n",
+    "\n",
+    "mask = np.tile(np.array(gold(nbits))[:,:,np.newaxis]*2 - 1, (1, 1, decimation)).reshape((2**nbits + 1, (2**nbits-1) * decimation))\n",
+    "print('mask', mask.shape)\n",
+    "\n",
+    "fig, (ax1, ax2) = plt.subplots(2, figsize=(16, 5))\n",
+    "fig.tight_layout()\n",
+    "corr_m = np.array([np.correlate(foo, row, mode='full') for row in mask])\n",
+    "#corr_m = np.array([row for row in mask])\n",
+    "ax1.matshow(corr_m, aspect='auto')\n",
+    "#ax.matshow(foo.reshape(32, 31)[::2,:])\n",
+    "ax2.matshow(correlate(bar, decimation=decimation), aspect='auto')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "bb32b5050ee14ddc8eb64697a8eb774b",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n",
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.image.AxesImage at 0x7ff8d8eb9e20>"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "decimation = 10\n",
+    "\n",
+    "fig, (ax1, ax2) = plt.subplots(2, figsize=(12, 5))\n",
+    "fig.tight_layout()\n",
+    "\n",
+    "#mask = np.tile(np.array(gold(nbits))[:,:,np.newaxis]*2 - 1, (1, 1, decimation)).reshape((2**nbits + 1, (2**nbits-1) * decimation))\n",
+    "#mask_stretched = np.tile(np.array(gold(nbits))[:,:,np.newaxis]*2 - 1, (1, 1, 1)).reshape((2**nbits + 1, (2**nbits-1) * 1))\n",
+    "\n",
+    "#ax1.matshow(mask)\n",
+    "#ax2.matshow(mask_stretched, aspect='auto')\n",
+    "\n",
+    "foo = np.repeat(modulate(np.array(list(range(4)))).astype(float), 1).reshape((4, 31))\n",
+    "foo_stretched = np.repeat(modulate(np.array(list(range(4)))).astype(float), 10).reshape(4, 310)\n",
+    "\n",
+    "ax1.matshow(foo)\n",
+    "ax2.matshow(foo_stretched, aspect='auto')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "48b3ae259e8046a5b90a82c4e80bab2e",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(31,) (31,)\n",
+      "(31,) (31,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(2.0, 1.0121324810255907)"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "decimation = 10\n",
+    "signal_amplitude = 2.0\n",
+    "nbits = 5\n",
+    "\n",
+    "foo = np.repeat(modulate(np.array([0, 1, 0, 0, 1, 1, 1, 0]), nbits) * 2.0 - 1, decimation) * signal_amplitude\n",
+    "noise = colorednoise.powerlaw_psd_gaussian(1, len(foo))\n",
+    "\n",
+    "sosh = sig.butter(4, 0.01, btype='highpass', output='sos', fs=decimation)\n",
+    "sosl = sig.butter(6, 1.0, btype='lowpass', output='sos', fs=decimation)\n",
+    "filtered = sig.sosfilt(sosh, sig.sosfilt(sosl, foo + noise))\n",
+    "#filtered = sig.sosfilt(sosh, foo + noise)\n",
+    "\n",
+    "fig, ((ax1, ax3), (ax2, ax4)) = plt.subplots(2, 2, figsize=(16, 9))\n",
+    "fig.tight_layout()\n",
+    "\n",
+    "ax1.plot(foo + noise)\n",
+    "ax1.plot(foo)\n",
+    "ax1.set_title('raw')\n",
+    "\n",
+    "ax2.plot(filtered)\n",
+    "ax2.plot(foo)\n",
+    "ax2.set_title('filtered')\n",
+    "\n",
+    "ax3.plot(correlate(foo + noise, nbits=nbits, decimation=decimation))\n",
+    "ax3.set_title('corr raw')\n",
+    " \n",
+    "ax3.grid()\n",
+    "\n",
+    "ax4.plot(correlate(filtered, nbits=nbits, decimation=decimation))\n",
+    "ax4.set_title('corr filtered')\n",
+    "ax4.grid()\n",
+    "\n",
+    "rms = lambda x: np.sqrt(np.mean(np.square(x)))\n",
+    "rms(foo), rms(noise)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "mean: 49.98625\n"
+     ]
+    }
+   ],
+   "source": [
+    "with open('/mnt/c/Users/jaseg/shared/raw_freq.bin', 'rb') as f:\n",
+    "    mains_noise = np.copy(np.frombuffer(f.read(), dtype='float32'))\n",
+    "    print('mean:', np.mean(mains_noise))\n",
+    "    mains_noise -= np.mean(mains_noise)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(63,) (63,)\n",
+      "(63,) (63,)\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "73f4caf6a80f448183c41b711412a471",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0.0020000000000000005, 0.014544699)"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "decimation = 10\n",
+    "signal_amplitude = 2.0e-3\n",
+    "nbits = 6\n",
+    "\n",
+    "#test_data = np.random.randint(0, 2, 100)\n",
+    "#test_data = np.array([0, 1, 0, 0, 1, 1, 1, 0])\n",
+    "test_data = np.random.RandomState(seed=0xcbb3b8cf).randint(0, 2 * (2**nbits), 128)\n",
+    "#test_data = np.random.RandomState(seed=0).randint(0, 8, 64)\n",
+    "#test_data = np.array(list(range(8)) * 8)\n",
+    "#test_data = np.array([0, 1] * 32)\n",
+    "#test_data = np.array(list(range(64)))\n",
+    "\n",
+    "foo = np.repeat(modulate(test_data, nbits) * 2.0 - 1, decimation) * signal_amplitude\n",
+    "noise = np.resize(mains_noise, len(foo))\n",
+    "#noise = 0\n",
+    "\n",
+    "sosh = sig.butter(3, 0.01, btype='highpass', output='sos', fs=decimation)\n",
+    "sosl = sig.butter(3, 0.8, btype='lowpass', output='sos', fs=decimation)\n",
+    "#filtered = sig.sosfilt(sosh, sig.sosfilt(sosl, foo + noise))\n",
+    "filtered = sig.sosfilt(sosh, foo + noise)\n",
+    "\n",
+    "cor1 = correlate(foo + noise, nbits=nbits, decimation=decimation)\n",
+    "#cor2 = correlate(filtered, nbits=nbits, decimation=decimation)\n",
+    "\n",
+    "#cor2_pe = correlate(filtered, nbits=nbits, decimation=decimation, mask_filter=lambda mask: sig.sosfilt(sosh, sig.sosfiltfilt(sosl, mask)))\n",
+    "\n",
+    "sosn = sig.butter(12, 4, btype='highpass', output='sos', fs=decimation)\n",
+    "#cor1_flt = sig.sosfilt(sosn, cor1)\n",
+    "#cor2_flt = sig.sosfilt(sosn, cor2)\n",
+    "#cor1_flt = cor1[1:] - cor1[:-1]\n",
+    "#cor2_flt = cor2[1:] - cor2[:-1]\n",
+    "\n",
+    "fig, ((ax1, ax3), (ax2, ax4)) = plt.subplots(2, 2, figsize=(16, 9))\n",
+    "fig.tight_layout()\n",
+    "\n",
+    "ax1.plot(foo + noise)\n",
+    "ax1.plot(foo)\n",
+    "ax1.set_title('raw')\n",
+    "ax1.grid(axis='y')\n",
+    "\n",
+    "ax2.plot(filtered)\n",
+    "ax2.plot(foo)\n",
+    "ax2.set_title('filtered')\n",
+    "ax2.grid(axis='y')\n",
+    "\n",
+    "for i in range(0, len(foo) + 1, decimation*(2**nbits - 1)):\n",
+    "    ax1.axvline(i, color='gray', alpha=0.5, lw=1)\n",
+    "    ax2.axvline(i, color='gray', alpha=0.5, lw=1)\n",
+    "\n",
+    "for i, (color, trace) in enumerate(zip(plt.cm.winter(np.linspace(0, 1, cor1.shape[0])), cor1.T)):\n",
+    "    if i%3 == 0:\n",
+    "        ax3.plot(trace + 0.5 * i, alpha=1.0, color=color)\n",
+    "ax3.set_title('corr raw')\n",
+    "ax3.grid()\n",
+    "\n",
+    "#ax4.plot(cor2[:4].T)\n",
+    "#ax4.set_title('corr filtered')\n",
+    "#ax4.grid()\n",
+    "ax4.matshow(cor1, aspect='auto')\n",
+    "\n",
+    "#ax5.plot(cor1_flt)\n",
+    "#ax5.set_title('corr raw (highpass)')\n",
+    "#ax5.grid()\n",
+    "\n",
+    "#ax6.plot(cor2_flt)\n",
+    "#ax6.set_title('corr filtered (highpass)')\n",
+    "#ax6.grid()\n",
+    "\n",
+    "#ax6.plot(cor2_pe[:4].T)\n",
+    "#ax6.set_title('corr filtered w/ mask preemphasis')\n",
+    "#ax6.grid()\n",
+    "\n",
+    "rms = lambda x: np.sqrt(np.mean(np.square(x)))\n",
+    "rms(foo), rms(noise)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "9fa8fa6a6837412da95630c634a12e21",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(63,) (63,)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7ff8ad6f3b50>]"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "\n",
+    "seq = np.repeat(gold(6)[29]*2 -1, decimation)\n",
+    "sosh = sig.butter(3, 0.01, btype='highpass', output='sos', fs=decimation)\n",
+    "sosl = sig.butter(3, 0.8, btype='lowpass', output='sos', fs=decimation)\n",
+    "seq_filtered = sig.sosfilt(sosh, sig.sosfiltfilt(sosl, seq))\n",
+    "#seq_filtered = sig.sosfilt(sosh, seq)\n",
+    "\n",
+    "ax.plot(seq)\n",
+    "ax.plot(seq_filtered)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "854dec05e45340ae91cf271b2facd7ed",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(63,) (63,)\n"
+     ]
+    },
+    {
+     "ename": "NameError",
+     "evalue": "name 'cor2_pe' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-24-f158dfc14cca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0msosh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbutter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'highpass'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'sos'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdecimation\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0msosl\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbutter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'lowpass'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'sos'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdecimation\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mcor2_pe_flt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msosfilt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msosh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcor2_pe\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0mcor2_pe_flt2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msosfilt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msosh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msosfiltfilt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msosl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcor2_pe\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'cor2_pe' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(3, 1, figsize=(9, 7), sharex=True)\n",
+    "fig.tight_layout()\n",
+    "axs = axs.flatten()\n",
+    "for ax in axs:\n",
+    "    ax.grid()\n",
+    "\n",
+    "seq = np.repeat(gold(6)[29]*2 -1, decimation)\n",
+    "sosh = sig.butter(3, 0.1, btype='highpass', output='sos', fs=decimation)\n",
+    "sosl = sig.butter(3, 0.8, btype='lowpass', output='sos', fs=decimation)\n",
+    "cor2_pe_flt = sig.sosfilt(sosh, cor2_pe)\n",
+    "cor2_pe_flt2 = sig.sosfilt(sosh, sig.sosfiltfilt(sosl, cor2_pe))\n",
+    "\n",
+    "axs[0].plot(cor2_pe)\n",
+    "axs[1].plot(cor2_pe_flt)\n",
+    "axs[2].plot(cor2_pe_flt2)\n",
+    "\n",
+    "#for idx in np.where(np.abs(cor2_pe_flt2) > 0.5)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b3f68635d3ad4863b990c0b6e742840b",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7ff8a9b7a820>]"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "nonlinear_distance = lambda x: 100**(2*np.abs(0.5-x%1)) / (np.abs(x)+3)**2\n",
+    "x = np.linspace(-1.5, 5.5, 10000)\n",
+    "ax.plot(x, nonlinear_distance(x))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "a6c4ef5b68a745b9963d3407df2e03fc",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "cor_an (65, 81269)\n",
+      "cwt_res (65, 81269)\n",
+      "th (65, 81269)\n",
+      "[((65,), (65,)), ((65,), (65,)), ((65,), (65,)), ((65,), (65,)), ((65,), (65,))]\n",
+      "peaks: 1852\n",
+      "avg_peak 1.6610203317347632\n",
+      "skipped 3 symbols at 42209.0\n",
+      "decoding [ref|dec]:\n",
+      " 10| 10 ✔     69| 69 ✔    124|124 ✔    102|102 ✔      2|  2 ✔      3|  3 ✔     78| 78 ✔     29| 29 ✔    \n",
+      "122|123 ✘     73| 73 ✔     98| 98 ✔     34| 34 ✔     -1| -1 ✔     97| 97 ✔      7|  7 ✔     97| 97 ✔    \n",
+      " 86| 86 ✔    120|120 ✔     95| 95 ✔     90| 90 ✔     49| 49 ✔     89| 89 ✔     83| 83 ✔     19| 19 ✔    \n",
+      " 84| 84 ✔    117|117 ✔     92| 92 ✔    119|119 ✔     16| 16 ✔     45| 45 ✔     23| 23 ✔     16| 16 ✔    \n",
+      "111|111 ✔      9|  9 ✔     89| 89 ✔     18| 18 ✔     36| 36 ✔      2|  2 ✔    115|115 ✔     40| 40 ✔    \n",
+      "100|100 ✔    105|105 ✔     93| 93 ✔     85| 85 ✔    107|107 ✔     90| 90 ✔     62| 62 ✔    116|116 ✔    \n",
+      " 42| 42 ✔    123|123 ✔     40| 40 ✔     -1| -1 ✔     77| 77 ✔     40| 40 ✔     57| 57 ✔    110|110 ✔    \n",
+      " 29| 29 ✔     94| 94 ✔      1|  1 ✔     29| 29 ✔     71| 71 ✔    119|119 ✔     15| 15 ✔    115|115 ✔    \n",
+      "120| -1       70| -1       50| 50 ✔     71| 71 ✔     50| 50 ✔     61| 61 ✔     38| 38 ✔      4|  4 ✔    \n",
+      "  3|  3 ✔    124|124 ✔     95| 95 ✔     27| 27 ✔     48| 48 ✔    116|116 ✔      3|  3 ✔     63| 63 ✔    \n",
+      " 19| 19 ✔     79| 79 ✔      2|  2 ✔     43| 43 ✔     92| 92 ✔      8|  8 ✔     65| 65 ✔     35| 35 ✔    \n",
+      " 30| 30 ✔     73| 73 ✔     73| 73 ✔     38| 38 ✔     58| 58 ✔     49| 49 ✔     45| 45 ✔     58| 58 ✔    \n",
+      " 46| 46 ✔    116|116 ✔    101|101 ✔      5|  5 ✔     78| 78 ✔    126|126 ✔    105| 76 ✘    108|108 ✔    \n",
+      " 59| 59 ✔     46| 46 ✔     27| 27 ✔     14| 14 ✔     57| 57 ✔     81| 81 ✔      3|  3 ✔      9|  9 ✔    \n",
+      "126|126 ✔     18| 55 ✘     76| 76 ✔    101|101 ✔    124|124 ✔      4|  4 ✔      3|  3 ✔    102|102 ✔    \n",
+      " 79| 79 ✔    121|121 ✔    103|103 ✔     92| 92 ✔     30| 30 ✔      4|  4 ✔    103|103 ✔     59| 58 ✘    \n",
+      "Symbol error rate e=0.046875\n",
+      "maximum bitrate r=321.6796875 b/h\n"
+     ]
+    }
+   ],
+   "source": [
+    "threshold_factor = 4.0\n",
+    "power_avg_width = 1024\n",
+    "max_lookahead = 6.5\n",
+    "\n",
+    "bit_period = (2**nbits) * decimation\n",
+    "peak_group_threshold = 0.1 * bit_period\n",
+    "\n",
+    "cor_an = cor1\n",
+    "\n",
+    "#fig, (ax1, ax2, ax3) = plt.subplots(3, figsize=(12, 12))\n",
+    "fig, (ax1, ax3) = plt.subplots(2, figsize=(12, 5))\n",
+    "fig.tight_layout()\n",
+    "\n",
+    "#ax1.matshow(sig.cwt(cor_an, sig.ricker, np.arange(1, 31)), aspect='auto')\n",
+    "\n",
+    "#for i in np.linspace(1, 10, 19):\n",
+    "#    offx = 5*i\n",
+    "#    ax2.plot(sig.cwt(cor_an, sig.ricker, [i]).flatten() + offx, color='red')\n",
+    "#\n",
+    "#    ax2.text(-50, offx, f'{i:.1f}',\n",
+    "#        horizontalalignment='right',\n",
+    "#        verticalalignment='center',\n",
+    "#        color='black')\n",
+    "#ax2.grid()\n",
+    "\n",
+    "ax3.grid()\n",
+    "print('cor_an', cor_an.shape)\n",
+    "\n",
+    "cwt_res = np.array([ sig.cwt(row, sig.ricker, [0.73 * decimation]).flatten() for row in cor_an ])\n",
+    "ax3.plot(cwt_res.T)\n",
+    "#def update(w = 1.0 * decimation):\n",
+    "#    line.set_ydata(sig.cwt(cor_an, sig.ricker, [w]).flatten())\n",
+    "#    fig.canvas.draw_idle()\n",
+    "#ipywidgets.interact(update)\n",
+    "\n",
+    "print('cwt_res', cwt_res.shape)\n",
+    "th = np.array([ np.convolve(np.abs(row), np.ones((power_avg_width,))/power_avg_width, mode='same') for row in cwt_res ])\n",
+    "ax1.plot(th.T)\n",
+    "print('th', th.shape)\n",
+    "\n",
+    "def compare_th(elem):\n",
+    "    idx, (th, val) = elem\n",
+    "    #print('compare_th:', th.shape, val.shape)\n",
+    "    return np.any(np.abs(val) > th*threshold_factor)\n",
+    "\n",
+    "print([ (a.shape, b.shape) for a, b in zip(th.T, cwt_res.T) ][:5])\n",
+    "\n",
+    "peaks = [ list(group) for val, group in itertools.groupby(enumerate(zip(th.T, cwt_res.T)), compare_th) if val ]\n",
+    "print('peaks:', len(peaks))\n",
+    "peak_group = []\n",
+    "for group in peaks:\n",
+    "    pos = np.mean([idx for idx, _val in group])\n",
+    "    pol = np.mean([max(val.min(), val.max(), key=abs) for _idx, (_th, val) in group])\n",
+    "    pol_idx = np.argmax(np.bincount([ np.argmax(np.abs(val)) for _idx, (_th, val) in group ]))\n",
+    "    #print(f'group', pos, pol, pol_idx)\n",
+    "    #for pol, (_idx, (_th, val)) in zip([max(val.min(), val.max(), key=abs) for _idx, (_th, val) in group], group):\n",
+    "    #    print('    ', pol, val)\n",
+    "    ax3.axvline(pos, color='cyan', alpha=0.3)\n",
+    "    \n",
+    "    if not peak_group or pos - peak_group[-1][1] > peak_group_threshold:\n",
+    "        if peak_group:\n",
+    "            peak_pos = peak_group[-1][3]\n",
+    "            ax3.axvline(peak_pos, color='red', alpha=0.6)\n",
+    "            #ax3.text(peak_pos-20, 2.0, f'{0 if pol < 0 else 1}', horizontalalignment='right', verticalalignment='center', color='black')\n",
+    "            \n",
+    "        peak_group.append((pos, pos, pol, pos, pol_idx))\n",
+    "        #ax3.axvline(pos, color='cyan', alpha=0.5)\n",
+    "        \n",
+    "    else:\n",
+    "        group_start, last_pos, last_pol, peak_pos, last_pol_idx = peak_group[-1]\n",
+    "    \n",
+    "        if abs(pol) > abs(last_pol):\n",
+    "            #ax3.axvline(pos, color='magenta', alpha=0.5)\n",
+    "            peak_group[-1] = (group_start, pos, pol, pos, pol_idx)\n",
+    "        else:\n",
+    "            #ax3.axvline(pos, color='blue', alpha=0.5)\n",
+    "            peak_group[-1] = (group_start, pos, last_pol, peak_pos, last_pol_idx)\n",
+    "\n",
+    "avg_peak = np.mean(np.abs(np.array([last_pol for _1, _2, last_pol, _3, _4 in peak_group])))\n",
+    "print('avg_peak', avg_peak)\n",
+    "\n",
+    "noprint = lambda *args, **kwargs: None\n",
+    "def mle_decode(peak_groups, print=print):\n",
+    "    peak_groups = [ (pos, pol, idx) for _1, _2, pol, pos, idx in peak_groups ]\n",
+    "    candidates = [ (0, [(pos, pol, idx)]) for pos, pol, idx in peak_groups if pos < bit_period*2.5 ]\n",
+    "    \n",
+    "    while candidates:\n",
+    "        chain_candidates = []\n",
+    "        for chain_score, chain in candidates:\n",
+    "            pos, ampl, _idx = chain[-1]\n",
+    "            score_fun = lambda pos, npos, npol: abs(npol)/avg_peak + nonlinear_distance((npos-pos)/bit_period)\n",
+    "            next_candidates = sorted([ (score_fun(pos, npos, npol), npos, npol, nidx) for npos, npol, nidx in peak_groups if pos < npos < pos + bit_period*max_lookahead ], reverse=True)\n",
+    "            \n",
+    "            print(f'    candidates for {pos}, {ampl}:')\n",
+    "            for score, npos, npol, nidx in next_candidates:\n",
+    "                print(f'        {score:.4f} {npos:.2f} {npol:.2f} {nidx:.2f}')\n",
+    "            \n",
+    "            nch, cor_len = cor_an.shape\n",
+    "            if cor_len - pos < 1.5*bit_period or not next_candidates:\n",
+    "                score = sum(score_fun(opos, npos, npol) for (opos, _opol, _oidx), (npos, npol, _nidx) in zip(chain[:-1], chain[1:])) / len(chain)\n",
+    "                yield score, chain\n",
+    "            \n",
+    "            else:\n",
+    "                print('extending')\n",
+    "                for score, npos, npol, nidx in next_candidates[:3]:\n",
+    "                    if score > 0.5:\n",
+    "                        new_chain_score = chain_score * 0.9 + score * 0.1\n",
+    "                        chain_candidates.append((new_chain_score, chain + [(npos, npol, nidx)]))\n",
+    "        print('chain candidates:')\n",
+    "        for score, chain in sorted(chain_candidates, reverse=True):\n",
+    "            print('    ', [(score, [(f'{pos:.2f}', f'{pol:.2f}') for pos, pol, _idx in chain])])\n",
+    "        candidates = [ (chain_score, chain) for chain_score, chain in sorted(chain_candidates, reverse=True)[:10] ]\n",
+    "\n",
+    "res = sorted(mle_decode(peak_group, print=noprint), reverse=True)\n",
+    "#for i, (score, chain) in enumerate(res):\n",
+    "#    print(f'Chain {i}@{score:.4f}: {chain}')\n",
+    "(_score, chain), *_ = res\n",
+    "\n",
+    "def viz(chain):\n",
+    "    last_pos = None\n",
+    "    for pos, pol, nidx in chain:\n",
+    "        if last_pos:\n",
+    "            delta = int(round((pos - last_pos) / bit_period))\n",
+    "            if delta > 1:\n",
+    "                print(f'skipped {delta} symbols at {pos}')\n",
+    "            for i in range(delta-1):\n",
+    "                yield None\n",
+    "        ax3.axvline(pos, color='blue', alpha=0.5)\n",
+    "        decoded = nidx*2 + (0 if pol < 0 else 1)\n",
+    "        yield decoded\n",
+    "        ax3.text(pos-20, 0.0, f'{decoded}', horizontalalignment='right', verticalalignment='center', color='black')\n",
+    "\n",
+    "        last_pos = pos\n",
+    "\n",
+    "decoded = list(viz(chain))\n",
+    "print('decoding [ref|dec]:')\n",
+    "failures = 0\n",
+    "for i, (ref, found) in enumerate(itertools.zip_longest(test_data, decoded)):\n",
+    "    print(f'{ref or -1:>3d}|{found or -1:>3d} {\"✔\" if ref==found else \"✘\" if found else \" \"}', end='    ')\n",
+    "    if ref != found:\n",
+    "        failures += 1\n",
+    "    if i%8 == 7:\n",
+    "        print()\n",
+    "print(f'Symbol error rate e={failures/len(test_data)}')\n",
+    "print(f'maximum bitrate r={sampling_rate / decimation / (2**nbits) * nbits * (1 - failures/len(test_data)) * 3600} b/h')\n",
+    "#ax3.plot(th)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "44d617eb7c5c416f96e16c9221c4fe96",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "ename": "NameError",
+     "evalue": "name 'cor2_pe_flt2' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-30-968181501cb1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0maxs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcor2_pe_flt2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcor2_pe_flt2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcor2_pe_flt2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcor2_pe_flt2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0maxs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'full'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'cor2_pe_flt2' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(2, 1, figsize=(9, 7))\n",
+    "fig.tight_layout()\n",
+    "axs = axs.flatten()\n",
+    "for ax in axs:\n",
+    "    ax.grid()\n",
+    "    \n",
+    "axs[0].plot(cor2_pe_flt2[1::10] - cor2_pe_flt2[:-1:10])\n",
+    "a, b = cor2_pe_flt2[1::10] - cor2_pe_flt2[:-1:10], np.array([0.0, -0.5, 1.0, -0.5, 0.0])\n",
+    "axs[1].plot(np.convolve(a, b, mode='full'))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/fec_experiments.ipynb

@@ -0,0 +1,529 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "from matplotlib import pyplot as plt\n",
+    "import pyldpc\n",
+    "import scipy.sparse"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "H, G = pyldpc.make_ldpc(384, 6, 8, systematic=False, seed=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(384, 101)"
+      ]
+     },
+     "execution_count": 116,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "n, k = G.shape\n",
+    "G.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 117,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "af5e3d32d4e7491ea2dfdceceef0b346",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(9, 6))\n",
+    "fig.tight_layout()\n",
+    "ax.matshow(H)\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 118,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import ctypes\n",
+    "lib = ctypes.CDLL('../controller/fw/ldpc_decoder_test.so')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 119,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.set_printoptions(linewidth=180, threshold=1000, edgeitems=20)\n",
+    "#bits_indices, bits, _ = scipy.sparse.find(H)\n",
+    "#np.all(bits_indices == np.repeat(range(288), 8))\n",
+    "bits_indices, bits, _ = scipy.sparse.find(H.T)\n",
+    "#p.bincount(bits_indices)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 120,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 120,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bits_indices, bits, _ = scipy.sparse.find(H)\n",
+    "l =  [                                                                                                                                                                                                                                                                                 0,    1,    2,    3,    4,    5,    6,    7,    8,    9,   10,   11,   12,   13,   14,   15,   16,   17,   18,   19,   20,   21,   22,   23,   24,   25,   26,   27,   28,   29,   30,   31\n",
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+    "    ,   64,   65,   66,   67,   68,   69,   70,   71,   72,   73,   74,   75,   76,   77,   78,   79,   80,   81,   82,   83,   84,   85,   86,   87,   88,   89,   90,   91,   92,   93,   94,   95\n",
+    "    ,   96,   97,   98,   99,  100,  101,  102,  103,  104,  105,  106,  107,  108,  109,  110,  111,  112,  113,  114,  115,  116,  117,  118,  119,  120,  121,  122,  123,  124,  125,  126,  127\n",
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+    "    ,   23,   51,  105,  143,  261,  289,  292,  330,   45,  148,  152,  171,  208,  238,  242,  303,   17,   91,  110,  231,  255,  271,  299,  372,   27,   87,   90,  129,  134,  236,  301,  352\n",
+    "    ,   40,  160,  180,  192,  229,  243,  273,  320,    9,   42,  115,  127,  157,  285,  349,  368,   68,   84,  170,  177,  232,  307,  321,  369,    3,   11,   57,  125,  147,  172,  283,  291\n",
+    "    ,    7,  190,  222,  227,  295,  348,  350,  359,   43,   69,   98,  101,  128,  207,  277,  293,   31,   55,  104,  119,  130,  158,  341,  375,   13,   85,  135,  226,  305,  318,  358,  366\n",
+    "    ,   22,   34,  183,  187,  199,  215,  311,  378,   32,   70,  112,  154,  205,  230,  266,  322,   54,  202,  248,  272,  290,  323,  343,  345,    0,   88,  150,  173,  233,  234,  269,  334\n",
+    "    ,  141,  146,  206,  220,  253,  281,  332,  381,   21,  138,  144,  174,  179,  194,  262,  298,   38,   71,   93,  156,  168,  181,  214,  239,   48,   50,   77,  264,  288,  328,  356,  357\n",
+    "    ,   96,  167,  184,  267,  280,  300,  347,  363,   14,   44,   80,  103,  145,  209,  335,  367,    2,    5,   74,  109,  121,  136,  151,  276,  131,  191,  195,  223,  286,  316,  377,  383\n",
+    "    ,    4,   39,  159,  235,  274,  306,  313,  346,    1,   24,   46,   52,   64,  123,  250,  259,   37,   59,  175,  185,  198,  251,  257,  340,  116,  118,  176,  244,  246,  265,  315,  374\n",
+    "    ,   26,   74,  124,  155,  189,  219,  374,  381,    4,   38,  103,  139,  199,  293,  319,  350,   75,   77,  158,  161,  181,  208,  261,  284,   39,  109,  122,  175,  234,  265,  271,  340\n",
+    "    ,    2,  130,  275,  277,  312,  333,  342,  362,   13,   31,   95,  209,  249,  289,  298,  375,   47,  125,  131,  164,  226,  252,  353,  356,   21,  159,  166,  324,  330,  339,  368,  383\n",
+    "    ,   10,   37,   89,  197,  220,  223,  300,  366,    0,   12,   78,  111,  112,  154,  311,  377,   86,  129,  140,  141,  191,  204,  254,  297,    3,   42,   61,  126,  185,  257,  269,  371\n",
+    "    ,   35,   43,  157,  210,  215,  251,  347,  367,   17,  177,  180,  193,  213,  263,  363,  372,   57,  104,  203,  227,  236,  253,  262,  344,   64,   72,   82,  135,  136,  239,  320,  348\n",
+    "    ,    1,  116,  218,  240,  288,  334,  357,  364,   20,   49,   97,  121,  182,  256,  294,  309,   79,  102,  113,  118,  137,  152,  195,  343,   23,   30,   48,  128,  216,  291,  313,  335\n",
+    "    ,   58,   63,  127,  169,  228,  264,  328,  369,   62,   70,  106,  144,  153,  198,  201,  255,   56,  107,  148,  162,  179,  212,  290,  351,   54,   59,   88,   92,  143,  282,  303,  365\n",
+    "    ,   99,  123,  165,  200,  222,  296,  302,  349,   15,   36,   50,   94,  160,  167,  230,  370,   73,  120,  138,  194,  231,  246,  259,  379,    9,   25,  146,  224,  260,  301,  359,  376\n",
+    "    ,  100,  183,  186,  238,  248,  258,  331,  352,  114,  117,  184,  188,  221,  268,  327,  378,  115,  192,  205,  214,  242,  325,  332,  382,   71,   84,   98,  174,  206,  235,  314,  317\n",
+    "    ,   19,   65,  101,  172,  196,  270,  316,  318,   28,   67,  119,  173,  202,  306,  341,  354,    7,   27,  247,  280,  285,  292,  321,  329,   60,   80,   93,  304,  310,  323,  336,  345\n",
+    "    ,   14,   52,   90,  132,  156,  276,  358,  380,   40,   91,  110,  171,  217,  233,  278,  281,   11,   66,  108,  149,  176,  241,  244,  283,   18,   32,   45,   87,  207,  245,  267,  307\n",
+    "    ,   22,   55,  142,  170,  187,  229,  308,  337,    6,   46,  134,  150,  178,  211,  250,  279,   16,  133,  266,  286,  315,  326,  338,  361,   24,   68,   76,   81,  225,  243,  295,  322\n",
+    "    ,    8,   41,   53,   69,   83,   96,  190,  237,   44,   51,  232,  272,  273,  287,  346,  355,    5,   29,   33,  147,  163,  274,  299,  360,   34,   85,  105,  145,  151,  168,  305,  373\n",
+    "    ,  126,  143,  197,  211,  267,  318,  326,  362,   26,  124,  200,  232,  265,  270,  298,  319,    5,   45,   48,  169,  203,  286,  351,  381,   24,   44,  123,  137,  156,  273,  283,  307\n",
+    "    ,   18,  108,  199,  234,  262,  275,  314,  375,    4,   37,   68,   75,  164,  264,  291,  295,   94,  183,  207,  221,  271,  289,  293,  354,  121,  131,  161,  166,  188,  259,  284,  327\n",
+    "    ,   10,   90,  127,  147,  244,  316,  328,  358,   11,   23,  122,  220,  288,  304,  325,  366,   63,   70,  101,  106,  146,  168,  195,  370,   52,  182,  218,  249,  330,  332,  333,  368\n",
+    "    ,   74,   97,  102,  239,  290,  308,  340,  373,   20,  110,  145,  163,  229,  246,  251,  331,   84,  136,  149,  213,  258,  301,  360,  365,   51,  114,  174,  238,  276,  348,  352,  383\n",
+    "    ,   13,   27,   30,   92,  187,  302,  338,  341,   62,   79,   80,  186,  230,  278,  294,  324,    9,   67,  180,  269,  285,  312,  343,  372,    7,   14,   83,   89,  160,  178,  287,  364\n",
+    "    ,   47,   56,   78,  107,  128,  177,  228,  250,   46,  100,  243,  252,  255,  282,  299,  345,   25,   28,   72,  162,  245,  257,  317,  382,   32,   36,   69,  115,  237,  342,  347,  355\n",
+    "    ,  105,  154,  179,  184,  268,  277,  346,  350,    6,   15,   55,  111,  113,  225,  297,  320,   21,   85,   86,  109,  261,  305,  344,  349,   22,  112,  125,  181,  216,  233,  281,  311\n",
+    "    ,   35,   38,   43,   82,  219,  263,  322,  380,   53,   57,   81,  117,  185,  247,  323,  367,   65,   66,  150,  165,  170,  235,  300,  357,    3,   29,  116,  144,  176,  196,  274,  306\n",
+    "    ,    2,   95,   98,  120,  141,  158,  193,  315,   64,   91,   99,  142,  248,  256,  279,  361,   60,  130,  167,  210,  236,  253,  254,  339,   59,   77,  129,  191,  202,  223,  296,  310\n",
+    "    ,    1,   16,   40,  140,  173,  209,  280,  353,   58,   73,   87,   96,  134,  208,  212,  313,   12,   42,   93,  119,  135,  272,  303,  329,   34,  118,  148,  189,  214,  222,  321,  337\n",
+    "    ,   54,   71,   88,  241,  356,  374,  376,  378,   39,   76,  157,  192,  205,  231,  266,  335,    8,  153,  155,  194,  204,  206,  359,  377,   17,   49,   61,  103,  133,  151,  336,  379\n",
+    "    ,   19,  172,  175,  190,  198,  201,  217,  227,    0,   31,   41,  104,  152,  159,  171,  309,   33,  132,  240,  242,  260,  292,  334,  369,   50,  138,  139,  215,  224,  226,  363,  371\n",
+    "\n",
+    "]\n",
+    "np.all(bits == l)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 121,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 121,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bits_indices, bits, _ = scipy.sparse.find(H.T)\n",
+    "l =  [\n",
+    "       0,   74,  108,  179,  201,  285,    0,   63,  113,  189,  208,  276,    0,   71,  116,  186,  196,  272,    0,   54,  105,  171,  203,  271,    0,   79,  141,  188,  193,  245,    0,   89\n",
+    "    ,  101,  186,  238,  242,    0,   86,  129,  159,  233,  265,    0,   70,   99,  172,  226,  259,    1,   82,  129,  156,  236,  282,    1,   84,  117,  169,  219,  258,    1,   59,  139,  145\n",
+    "    ,  200,  248,    1,   94,  121,  171,  230,  249,    1,   85,  134,  145,  201,  278,    1,   73,   97,  175,  197,  256,    1,   56,  116,  185,  228,  259,    1,   65,  122,  159,  217,  265\n",
+    "    ,    2,   94,   99,  144,  234,  276,    2,   82,  130,  166,  205,  283,    2,   78,  103,  152,  231,  244,    2,   91,   98,  161,  224,  284,    2,   85,  141,  150,  209,  253,    2,   69\n",
+    "    ,  103,  181,  199,  266,    2,   92,  139,  176,  232,  267,    2,   67,  125,  164,  211,  249,    3,   56,  142,  189,  235,  243,    3,   77,   97,  151,  219,  262,    3,   91,  141,  154\n",
+    "    ,  192,  241,    3,   75,  143,  167,  226,  256,    3,   86,  117,  151,  225,  262,    3,   93,  115,  151,  238,  271,    3,   87,  121,  148,  211,  256,    3,   77,  127,  174,  197,  285\n",
+    "    ,    4,   52,  113,  177,  231,  263,    4,   48,  125,  147,  238,  286,    4,   48,  108,  176,  239,  279,    4,   91,  141,  159,  204,  268,    4,   53,   97,  160,  217,  263,    4,   88\n",
+    "    ,  135,  190,  200,  245,    4,   65,  143,  182,  193,  268,    4,   55,  111,  188,  195,  281,    5,   88,  115,  168,  229,  276,    5,   67,  119,  149,  236,  285,    5,   49,   97,  169\n",
+    "    ,  203,  278,    5,   51,  105,  173,  204,  268,    5,   83,  131,  185,  237,  243,    5,   67,  114,  165,  231,  242,    5,   55,  115,  189,  233,  261,    5,   70,  143,  146,  198,  260\n",
+    "    ,    6,   66,   96,  183,  211,  242,    6,   49,  137,  148,  209,  283,    6,   54,   96,  183,  217,  287,    6,   76,  102,  164,  237,  255,    6,   48,   98,  189,  228,  251,    6,   57\n",
+    "    ,  143,  159,  236,  269,    6,   57,  128,  178,  215,  280,    6,   48,  107,  174,  232,  265,    7,   79,  142,  148,  214,  260,    7,   80,  120,  171,  206,  269,    7,   91,  101,  148\n",
+    "    ,  212,  277,    7,   77,  125,  190,  215,  275,    7,   66,  100,  149,  227,  274,    7,   50,  110,  148,  203,  283,    7,   68,  130,  150,  213,  257,    7,   61,  139,  163,  212,  250\n",
+    "    ,    8,   77,  106,  189,  207,  273,    8,   81,  122,  155,  224,  270,    8,   57,  130,  161,  230,  270,    8,   75,   98,  148,  225,  258,    8,   83,  136,  170,  235,  245,    8,   56\n",
+    "    ,  128,  173,  236,  263,    8,   54,  118,  177,  213,  250,    8,   93,  132,  182,  223,  280,    9,   73,  133,  155,  207,  262,    9,   60,  142,  146,  218,  277,    9,   78,  117,  186\n",
+    "    ,  192,  252,    9,   91,  101,  152,  194,  245,    9,   72,  104,  149,  235,  281,    9,   55,  134,  183,  194,  275,    9,   49,  114,  163,  201,  260,    9,   69,  106,  150,  210,  257\n",
+    "    ,   10,   83,  139,  185,  227,  257,   10,   75,  138,  157,  235,  269,   10,   83,  122,  144,  207,  268,   10,   64,   98,  157,  236,  259,   10,   75,  137,  170,  223,  254,   10,   55\n",
+    "    ,  125,  175,  239,  266,   10,   86,  110,  153,  202,  266,   10,   81,  124,  167,  231,  277,   11,   58,  102,  179,  215,  280,   11,   92,  108,  149,  200,  259,   11,   60,  124,  167\n",
+    "    ,  228,  248,   11,   59,  100,  166,  229,  273,   11,   85,  114,  146,  215,  256,   11,   50,  100,  182,  227,  278,   11,   67,  128,  163,  217,  246,   11,   64,  120,  146,  197,  272\n",
+    "    ,   12,   68,   97,  184,  236,  277,   12,   54,  104,  162,  209,  252,   12,   94,  118,  173,  223,  272,   12,   89,  116,  163,  216,  273,   12,   59,   96,  157,  220,  261,   12,   63\n",
+    "    ,   97,  173,  224,  250,   12,   86,  121,  147,  210,  252,   12,   73,  134,  185,  193,  283,   13,   85,  113,  174,  206,  285,   13,   65,  113,  164,  239,  264,   13,   50,  129,  161\n",
+    "    ,  213,  250,   13,   76,  123,  146,  214,  260,   13,   79,  101,  151,  230,  244,   13,   87,  125,  186,  195,  266,   13,   74,  140,  166,  229,  253,   13,   64,  123,  157,  201,  265\n",
+    "    ,   14,   69,  109,  177,  201,  267,   14,   56,  106,  150,  210,  265,   14,   75,  118,  161,  221,  255,   14,   49,  123,  169,  222,  263,   14,   60,  141,  191,  208,  271,   14,   85\n",
+    "    ,  127,  152,  221,  269,   14,   80,  111,  191,  210,  279,   14,   86,  118,  174,  225,  278,   15,   95,  104,  152,  218,  272,   15,   50,  102,  186,  209,  247,   15,   72,  129,  157\n",
+    "    ,  195,  249,   15,   66,  130,  189,  216,  243,   15,   62,  140,  145,  192,  241,   15,   69,  112,  171,  198,  267,   15,   79,  120,  145,  203,  240,   15,   62,  110,  169,  212,  248\n",
+    "    ,   16,   76,  100,  173,  211,  260,   16,   60,  119,  167,  202,  275,   16,   68,  102,  174,  196,  274,   16,   75,  126,  187,  198,  247,   16,   66,  133,  147,  228,  286,   16,   62\n",
+    "    ,  142,  152,  234,  283,   16,   87,  120,  167,  233,  277,   16,   63,  138,  175,  207,  278,   17,   77,  105,  186,  207,  254,   17,   78,  104,  153,  210,  243,   17,   71,  109,  181\n",
+    "    ,  218,  287,   17,   65,  102,  161,  193,  287,   17,   80,  133,  148,  202,  276,   17,   63,  111,  180,  202,  272,   17,   85,  106,  144,  232,  273,   17,   83,  132,  164,  215,  240\n",
+    "    ,   18,   81,  138,  181,  213,  271,   18,   64,  131,  185,  239,  253,   18,   52,  140,  180,  219,  250,   18,   93,  115,  171,  238,  248,   18,   52,  110,  165,  214,  279,   18,   74\n",
+    "    ,  125,  153,  230,  254,   18,   60,  119,  179,  233,  270,   18,   58,  118,  186,  239,  283,   19,   77,  140,  165,  210,  285,   19,   69,  127,  151,  213,  282,   19,   70,  108,  177\n",
+    "    ,  201,  264,   19,   94,  114,  157,  192,  282,   19,   76,  116,  182,  228,  243,   19,   90,  103,  169,  204,  281,   19,   61,  104,  174,  194,  272,   19,   53,  134,  188,  199,  285\n",
+    "    ,   20,   86,  115,  168,  217,  259,   20,   95,  128,  161,  194,  247,   20,   72,   98,  153,  214,  262,   20,   57,  132,  154,  238,  253,   20,   65,  127,  147,  198,  245,   20,   93\n",
+    "    ,  126,  162,  216,  270,   20,   91,  137,  160,  199,  247,   20,   71,  132,  184,  217,  274,   21,   51,  103,  182,  239,  250,   21,   82,  137,  151,  212,  242,   21,   54,  101,  170\n",
+    "    ,  232,  270,   21,   87,  133,  165,  229,  285,   21,   90,  101,  171,  224,  284,   21,   51,  135,  179,  225,  276,   21,   79,  103,  181,  223,  255,   21,   88,  140,  190,  195,  284\n",
+    "    ,   22,   67,  132,  191,  230,  271,   22,   75,  129,  170,  205,  260,   22,   93,  113,  154,  233,  259,   22,   65,  133,  181,  214,  264,   22,   82,  112,  168,  205,  258,   22,   76\n",
+    "    ,  111,  182,  194,  267,   22,   86,  122,  158,  209,  251,   22,   81,  141,  176,  220,  246,   23,   52,  142,  184,  221,  264,   23,   95,  114,  190,  203,  269,   23,   77,  128,  150\n",
+    "    ,  220,  257,   23,   79,   98,  176,  232,  256,   23,   79,   99,  161,  221,  247,   23,   53,  113,  158,  192,  279,   23,   74,  100,  172,  236,  284,   23,   64,  106,  187,  202,  275\n",
+    "    ,   24,   59,  126,  168,  222,  281,   24,   61,  133,  156,  205,  272,   24,   68,  105,  181,  218,  282,   24,   90,  141,  187,  210,  250,   24,   80,  126,  158,  224,  271,   24,   78\n",
+    "    ,  130,  156,  200,  240,   24,   50,  109,  190,  213,  284,   24,   82,  127,  176,  193,  244,   25,   57,  132,  153,  216,  241,   25,   83,  108,  145,  213,  284,   25,   76,  134,  178\n",
+    "    ,  225,  275,   25,   56,  135,  159,  206,  242,   25,   78,  124,  160,  202,  282,   25,   95,  129,  177,  222,  281,   25,   94,  131,  180,  223,  282,   25,   74,   99,  173,  231,  246\n",
+    "    ,   26,   68,  136,  165,  194,  277,   26,   61,  142,  185,  197,  276,   26,   68,  104,  144,  204,  274,   26,   58,  126,  162,  233,  240,   26,   71,  122,  146,  214,  277,   26,   95\n",
+    "    ,  127,  150,  205,  254,   26,   62,  116,  182,  222,  279,   26,   94,  119,  176,  204,  287,   27,   71,  136,  155,  211,  267,   27,   74,  129,  144,  229,  284,   27,   95,  100,  149\n",
+    "    ,  208,  251,   27,   61,  107,  155,  192,  268,   27,   66,  135,  180,  200,  249,   27,   67,  120,  147,  221,  246,   27,   67,  127,  172,  216,  279,   27,   50,  111,  187,  200,  275\n",
+    "    ,   28,   88,  119,  162,  219,  287,   28,   57,  115,  156,  235,  265,   28,   61,  130,  175,  198,  287,   28,   87,  139,  172,  206,  284,   28,   73,  139,  157,  212,  260,   28,   87\n",
+    "    ,  135,  168,  232,  253,   28,   65,  121,  177,  217,  257,   28,   95,  135,  166,  218,  281,   29,   48,  106,  170,  237,  241,   29,   60,  136,  179,  229,  267,   29,   49,   97,  179\n",
+    "    ,  195,  244,   29,   55,  116,  188,  223,  270,   29,   77,  126,  167,  206,  274,   29,   56,  131,  159,  236,  263,   29,   86,  117,  165,  220,  255,   29,   72,  131,  182,  207,  252\n",
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+    "    ,   44,   89,   98,  167,  220,  255,   44,   72,  104,  145,  198,  276,   44,   78,  133,  162,  225,  246,   44,   62,  111,  150,  237,  263,   44,   81,  128,  183,  198,  280,   44,   57\n",
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+    "    ,  196,  240,   45,   69,   96,  184,  205,  287,   45,   94,  138,  151,  208,  259,   45,   52,  110,  160,  215,  254,   45,   72,  134,  175,  200,  249,   45,   87,   99,  185,  204,  269\n",
+    "    ,   46,   59,  119,  169,  199,  251,   46,   56,  140,  170,  212,  286,   46,   58,  140,  144,  217,  250,   46,   84,  130,  154,  203,  287,   46,   78,  115,  166,  205,  258,   46,   82\n",
+    "    ,  102,  160,  239,  252,   46,   74,   99,  191,  192,  280,   46,   49,  138,  174,  197,  244,   47,   92,  134,  163,  219,  280,   47,   72,  108,  187,  201,  282,   47,   79,   96,  176\n",
+    "    ,  221,  280,   47,   88,  131,  159,  218,  283,   47,   72,  114,  154,  228,  268,   47,   62,  125,  180,  192,  242,   47,   53,  142,  162,  222,  262,   47,   69,  103,  187,  199,  255\n",
+    "\n",
+    "]\n",
+    "np.all(bits == l)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 122,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(288, 384)"
+      ]
+     },
+     "execution_count": 122,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 123,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2304"
+      ]
+     },
+     "execution_count": 123,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.sum(H)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 124,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "110592"
+      ]
+     },
+     "execution_count": 124,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(H.flatten())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 125,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 125,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "6 * 384 == 8*288"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 126,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
+       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6])"
+      ]
+     },
+     "execution_count": 126,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.sum(H, axis=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 127,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n",
+       "       8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n",
+       "       8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n",
+       "       8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n",
+       "       8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n",
+       "       8, 8, 8])"
+      ]
+     },
+     "execution_count": 127,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.sum(H, axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 128,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "7612cc62e7f34f70a0a93ed84b88fe79",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.image.AxesImage at 0x7fc70960cac0>"
+      ]
+     },
+     "execution_count": 128,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "test_data = np.random.randint(0, 2, k)\n",
+    "\n",
+    "d = np.dot(G, test_data) % 2\n",
+    "x = (-1) ** d\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(9, 3))\n",
+    "ax.matshow(x.reshape((-1, 64)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 129,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((384,), (101,))"
+      ]
+     },
+     "execution_count": 129,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x.shape, test_data.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 130,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 130,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.all(np.equal(pyldpc.get_message(G, pyldpc.decode(H, x, 3)), test_data))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/gauss_derivations.ipynb

@@ -0,0 +1,184 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "\\[\\tag{${\\it \\%o}_{2}$}f\\left(a , \\mu , \\sigma , x\\right):=a\\,\\exp \\left(\\frac{-\\left(x-\\mu\\right)^2}{2\\,\\sigma^2}\\right)\\]"
+      ],
+      "text/plain": [
+       "                                                         2\n",
+       "                                               - (x - mu)\n",
+       "(%o2)              f(a, mu, sigma, x) := a exp(-----------)\n",
+       "                                                       2\n",
+       "                                                2 sigma"
+      ],
+      "text/x-maxima": [
+       "f(a,mu,sigma,x):=a*exp((-(x-mu)^2)/(2*sigma^2))"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "f(a, mu, sigma, x) := a*exp(-(x-mu)^2/(2*sigma^2));"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "\\[\\tag{${\\it \\%o}_{11}$}-\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]"
+      ],
+      "text/plain": [
+       "                                                   2\n",
+       "                                           (x - mu)\n",
+       "                                         - ---------\n",
+       "                                                  2\n",
+       "                                           2 sigma\n",
+       "                            a (x - mu) %e\n",
+       "(%o11)                    - ------------------------\n",
+       "                                          2\n",
+       "                                     sigma"
+      ],
+      "text/x-maxima": [
+       "-(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diff(f(a, mu, sigma, x), x);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "\\[\\tag{${\\it \\%o}_{12}$}e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }\\]"
+      ],
+      "text/plain": [
+       "                                             2\n",
+       "                                     (x - mu)\n",
+       "                                   - ---------\n",
+       "                                            2\n",
+       "                                     2 sigma\n",
+       "(%o12)                           %e"
+      ],
+      "text/x-maxima": [
+       "%e^-((x-mu)^2/(2*sigma^2))"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diff(f(a, mu, sigma, x), a);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "\\[\\tag{${\\it \\%o}_{13}$}\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]"
+      ],
+      "text/plain": [
+       "                                                  2\n",
+       "                                          (x - mu)\n",
+       "                                        - ---------\n",
+       "                                                 2\n",
+       "                                          2 sigma\n",
+       "                           a (x - mu) %e\n",
+       "(%o13)                     ------------------------\n",
+       "                                         2\n",
+       "                                    sigma"
+      ],
+      "text/x-maxima": [
+       "(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diff(f(a, mu, sigma, x), mu);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "\\[\\tag{${\\it \\%o}_{14}$}\\frac{a\\,\\left(x-\\mu\\right)^2\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^3}\\]"
+      ],
+      "text/plain": [
+       "                                                   2\n",
+       "                                           (x - mu)\n",
+       "                                         - ---------\n",
+       "                                                  2\n",
+       "                                     2     2 sigma\n",
+       "                           a (x - mu)  %e\n",
+       "(%o14)                     -------------------------\n",
+       "                                         3\n",
+       "                                    sigma"
+      ],
+      "text/x-maxima": [
+       "(a*(x-mu)^2*%e^-((x-mu)^2/(2*sigma^2)))/sigma^3"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diff(f(a, mu, sigma, x), sigma);"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Maxima",
+   "language": "maxima",
+   "name": "maxima"
+  },
+  "language_info": {
+   "codemirror_mode": "maxima",
+   "file_extension": ".mac",
+   "mimetype": "text/x-maxima",
+   "name": "maxima",
+   "pygments_lexer": "maxima",
+   "version": "5.43.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/grid_frequency_spectra.ipynb

@@ -0,0 +1,399 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import csv\n",
+    "\n",
+    "import numpy as np\n",
+    "from matplotlib import pyplot as plt\n",
+    "import scipy.fftpack"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data = np.genfromtxt('data/Netzfrequenz_Sekundenwerte_2012_KW37.csv', delimiter=',')[1:,1:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "171a6975a39e48bcac5e1247903b70f4",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f0144563d30>]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(data[:3600*24, 0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.02051102806199375"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.std(data[:,0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2b835c8fb082428cabc1ad9112286728",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(1e-06, 0.5)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Number of samplepoints\n",
+    "N = len(data[:,0])\n",
+    "# sample spacing\n",
+    "T = 1.0\n",
+    "x = np.linspace(0.0, N*T, N)\n",
+    "yf = scipy.fftpack.fft(data[:,0])\n",
+    "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
+    "\n",
+    "yf = 2.0/N * np.abs(yf[:N//2])\n",
+    "\n",
+    "#yf = sum(yf[s::10] for s in range(10)) / 10\n",
+    "#xf = sum(xf[s::10] for s in range(10)) / 10\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xf, yf)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
+    "ax.set_xlabel('T in s')\n",
+    "ax.set_ylabel('Amplitude Δf')\n",
+    "ax.grid()\n",
+    "ax.set_xlim([1/1000000, 0.5])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "94ca3cb49e7d452dab8f7e2e8d632b84",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(5e-07, 0.02)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Number of samplepoints\n",
+    "N = len(data[:,0])\n",
+    "# sample spacing\n",
+    "T = 1.0\n",
+    "x = np.linspace(0.0, N*T, N)\n",
+    "yf = scipy.fftpack.fft(data[:,0])\n",
+    "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
+    "\n",
+    "yf = 2.0/N * np.abs(yf[:N//2])\n",
+    "\n",
+    "average_from = lambda val, start, average_width: np.hstack([val[:start], [ np.mean(val[i:i+average_width]) for i in range(start, len(val), average_width) ]])\n",
+    "\n",
+    "average_width = 20\n",
+    "average_start = 100\n",
+    "yf = average_from(yf, average_start, average_width)\n",
+    "xf = average_from(xf, average_start, average_width)\n",
+    "yf = average_from(yf, 300, average_width)\n",
+    "xf = average_from(xf, 300, average_width)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xf, yf)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
+    "ax.set_xlabel('T in s')\n",
+    "ax.set_ylabel('Amplitude Δf')\n",
+    "\n",
+    "for i, t in enumerate([45, 60, 600, 1200, 1800, 3600]):\n",
+    "    ax.axvline(1/t, color='red', alpha=0.5)\n",
+    "    ax.annotate(f'{t} s', xy=(1/t, 3e-3), xytext=(-15, 0), xycoords='data', textcoords='offset pixels', rotation=90)\n",
+    "#ax.text(1/60, 10,'60 s', ha='left')\n",
+    "ax.grid()\n",
+    "ax.set_xlim([1/60000, 0.5])\n",
+    "ax.set_ylim([5e-7, 2e-2])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "91a04300b9164bd7a9915d0028f3e563",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ys = scipy.fftpack.fft(data[:,0])\n",
+    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
+    "s = 60\n",
+    "\n",
+    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
+    "\n",
+    "xs = np.linspace(0, 1.0/2.0, len(data)//2)\n",
+    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xs[s//2:-s//2+1], ys)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2811a79d4ad8487f822750e4419ccfdb",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ys = scipy.fftpack.fft(data[:,0])\n",
+    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
+    "s = 1\n",
+    "\n",
+    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
+    "\n",
+    "xs = np.linspace(0, 1.0/2.0, len(data)//2)\n",
+    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xs[s//2:-s//2+1 if s > 1 else None], ys)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "c678197e011e4ab4982d3e1d2a2cee9a",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ys = scipy.fftpack.fft(data[:,0])\n",
+    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
+    "s = 1\n",
+    "\n",
+    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
+    "\n",
+    "xs = np.linspace(0, 1.0/2.0, len(data)//2)\n",
+    "\n",
+    "ys *= 2*np.pi*xs\n",
+    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xs[s//2:-s//2+1 if s > 1 else None], ys)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "52bcd29a41a54ed1bf9dc63e0c9e83d8",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ys = scipy.fftpack.fft(data[:,0])\n",
+    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
+    "s = 30\n",
+    "\n",
+    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
+    "\n",
+    "xs = np.linspace(0, 1.0/2.0, len(data)//2)\n",
+    "\n",
+    "ys *= 2*np.pi*xs[s//2:-s//2+1]\n",
+    "\n",
+    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(9,5))\n",
+    "ax.loglog(xs[s//2:-s//2+1], ys)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
+    "ax.grid()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "15.923566878980893"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "1/0.0628"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/grid_scope.ipynb

@@ -0,0 +1,726 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Grid frequency estimation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "import sqlite3\n",
+    "import struct\n",
+    "import datetime\n",
+    "import scipy.fftpack\n",
+    "from scipy import signal as sig\n",
+    "\n",
+    "import matplotlib\n",
+    "from matplotlib import pyplot as plt\n",
+    "from matplotlib import patches\n",
+    "import numpy as np\n",
+    "from scipy import signal, optimize\n",
+    "from tqdm.notebook import tnrange, tqdm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step 1: Setup\n",
+    "### Load data series information from sqlite capture file\n",
+    "\n",
+    "One capture file may contain multiple runs/data series. Display a list of runs and their start/end time and sample count, then select the newest one in `last_run` variable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "db = sqlite3.connect('data/waveform-raspi-ocxo-2.sqlite3')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Run 000: 2020-04-01 14:00:25 - 2020-04-01 15:09:31 (  1:09:05.846,   4197664sp)\n",
+      "Run 001: 2020-04-02 11:56:41 - 2020-04-02 11:57:59 (  0:01:18.544,     79552sp)\n",
+      "Run 002: 2020-04-02 12:03:51 - 2020-04-02 12:12:54 (  0:09:03.033,    549792sp)\n"
+     ]
+    }
+   ],
+   "source": [
+    "for run_id, start, end, count in db.execute('SELECT run_id, MIN(rx_ts), MAX(rx_ts), COUNT(*) FROM measurements GROUP BY run_id'):\n",
+    "    foo = lambda x: datetime.datetime.fromtimestamp(x/1000)\n",
+    "    start, end = foo(start), foo(end)\n",
+    "    print(f'Run {run_id:03d}: {start:%Y-%m-%d %H:%M:%S} - {end:%Y-%m-%d %H:%M:%S} ({str(end-start)[:-3]:>13}, {count*32:>9d}sp)')\n",
+    "last_run, n_records = run_id, count"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Setup analog parameters\n",
+    "\n",
+    "Setup parameters of analog capture hardware here. This is used to scale samples from ADC counts to analog voltages. Also setup sampling rate here. Nominal sampling rate is 1 ksps."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sampling_rate = 1000.0 * 48.6 / 48\n",
+    "\n",
+    "par = lambda *rs: 1/sum(1/r for r in rs) # resistor parallel calculation\n",
+    "\n",
+    "# Note: These are for the first prototype only!\n",
+    "vmeas_source_impedance = 330e3\n",
+    "vmeas_source_scale = 0.5\n",
+    "\n",
+    "vcc = 15.0\n",
+    "vmeas_div_high = 27e3\n",
+    "vmeas_div_low = par(4.7e3, 10e3)\n",
+    "vmeas_div_voltage = vcc * vmeas_div_low / (vmeas_div_high + vmeas_div_low)\n",
+    "vmeas_div_impedance = par(vmeas_div_high, vmeas_div_low)\n",
+    "\n",
+    "#vmeas_overall_factor = vmeas_div_impedance / (vmeas_source_impedance + vmeas_div_impedance)\n",
+    "v0 = 1.5746\n",
+    "v100 = 2.004\n",
+    "vn100 = 1.1452\n",
+    "\n",
+    "adc_vcc = 3.3 # V\n",
+    "adc_fullscale = 4095\n",
+    "\n",
+    "adc_val_to_voltage_factor = 1/adc_fullscale * adc_vcc\n",
+    "\n",
+    "adc_count_to_vmeas = lambda x: (x*adc_val_to_voltage_factor - v0) / (v100-v0) * 100"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Load run data from sqlite3 capture file\n",
+    "\n",
+    "Load measurement data for the selected run and assemble a numpy array containing one continuous trace. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "fa875d84971946ada24a959c1a85fe78",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "HBox(children=(FloatProgress(value=0.0, max=17181.0), HTML(value='')))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "RMS voltage: 228.5564548966498\n"
+     ]
+    }
+   ],
+   "source": [
+    "limit = n_records\n",
+    "record_size = 32\n",
+    "skip_dropped_sections = False\n",
+    "\n",
+    "data = np.zeros(limit*record_size)\n",
+    "data[:] = np.nan\n",
+    "\n",
+    "last_seq = None\n",
+    "write_index = 0\n",
+    "for i, (seq, chunk) in tqdm(enumerate(db.execute(\n",
+    "        'SELECT seq, data FROM measurements WHERE run_id = ? ORDER BY rx_ts LIMIT ? OFFSET ?',\n",
+    "        (last_run, limit, n_records-limit))), total=n_records):\n",
+    "    \n",
+    "    if last_seq is None or seq == (last_seq + 1)%0x10000:\n",
+    "        last_seq = seq\n",
+    "        idx = write_index if skip_dropped_sections else i\n",
+    "        data[idx*record_size:(idx+1)*record_size] = np.frombuffer(chunk, dtype='<H')\n",
+    "        write_index += 1\n",
+    "        \n",
+    "    elif seq > last_seq:\n",
+    "        last_seq = seq\n",
+    "        # nans = np.empty((record_size,))\n",
+    "        # nans[:] = np.nan\n",
+    "        # data = np.append(data, nans) FIXME\n",
+    "        \n",
+    "data = (data * adc_val_to_voltage_factor - v0) / (v100-v0) * 100\n",
+    "\n",
+    "# https://stackoverflow.com/questions/6518811/interpolate-nan-values-in-a-numpy-array\n",
+    "nan_helper = lambda y: (np.isnan(y), lambda z: z.nonzero()[0])\n",
+    "\n",
+    "# data rarely may contain NaNs where the capture script failed to read and acknowledge capture buffers from the sensor board fast enough.\n",
+    "# For RMS calculation and overall FFT fill these NaNs with interpolated values from their neighbors.\n",
+    "data_not_nan = np.copy(data)\n",
+    "nans, x = nan_helper(data)\n",
+    "data_not_nan[nans]= np.interp(x(nans), x(~nans), data[~nans])\n",
+    "\n",
+    "print('RMS voltage:', np.sqrt(np.mean(np.square(data_not_nan))))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Show a preview of loaded data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2cf087d340f7461d88d2ebaba0c6f95e",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, (top, bottom) = plt.subplots(2, figsize=(9,6))\n",
+    "fig.tight_layout(pad=3, h_pad=1.8)\n",
+    "\n",
+    "range_start, range_len = -300, 60 # [s]\n",
+    "\n",
+    "data_slice = data[ int(range_start * sampling_rate) : int((range_start + range_len) * sampling_rate) ]\n",
+    "\n",
+    "top.grid()\n",
+    "top.plot(np.linspace(0, range_len, int(range_len*sampling_rate)), data_slice, lw=1.0)\n",
+    "top.set_xlim([range_len/2-0.25, range_len/2+0.25])\n",
+    "mean = np.mean(data_not_nan)\n",
+    "rms = np.sqrt(np.mean(np.square(data_not_nan - mean)))\n",
+    "peak = np.max(np.abs(data_not_nan - mean))\n",
+    "top.axhline(mean, color='red')\n",
+    "bbox = {'facecolor': 'black', 'alpha': 0.8, 'pad': 2}\n",
+    "top.text(0.02, 0.5, f'mean: {mean:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='left', va='center')\n",
+    "top.text(0.98, 0.2, f'V_RMS: {rms:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='right')\n",
+    "top.text(0.98, 0.1, f'V_Pk: {peak:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='right')\n",
+    "top.text(0.5, 0.9, f'Run {run_id}', transform=top.transAxes, color='white', bbox=bbox, ha='center', fontweight='bold')\n",
+    "\n",
+    "bottom.grid()\n",
+    "bottom.specgram(data_slice, Fs=sampling_rate)\n",
+    "top.set_ylabel('U [V]')\n",
+    "bottom.set_ylabel('F [Hz]')\n",
+    "bottom.set_xlabel('t [s]')\n",
+    "\n",
+    "top.set_title('Voltage waveform')\n",
+    "bottom.set_title('Voltage frequency spectrum')\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step 2: Calculate Short-Time Fourier Transform of capture"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Window length: 202 sp, zero-padded to 202 sp\n"
+     ]
+    }
+   ],
+   "source": [
+    "fs = sampling_rate # Hz\n",
+    "ff = 50 # Hz\n",
+    "\n",
+    "analysis_periods = 10\n",
+    "window_len = fs * analysis_periods/ff\n",
+    "nfft_factor = 1\n",
+    "sigma = window_len/8 # samples\n",
+    "\n",
+    "f, t, Zxx = signal.stft(data,\n",
+    "            fs = fs,\n",
+    "            window=('gaussian', sigma),\n",
+    "            nperseg = window_len,\n",
+    "            nfft = window_len * nfft_factor)\n",
+    "print(f'Window length: {window_len:.0f} sp, zero-padded to {window_len * nfft_factor:.0f} sp')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Show a preview of STFT results\n",
+    "\n",
+    "Cut out our approximate frequency range of interest"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "432082c0f3a644d781669c57e8324ceb",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(9, 3))\n",
+    "fig.tight_layout(pad=2, h_pad=0.1)\n",
+    "\n",
+    "ax.pcolormesh(t[-200:-100], f[:250], np.abs(Zxx[:250,-200:-100]))\n",
+    "ax.set_title(f\"Run {last_run}\", pad=-20, color='white')\n",
+    "ax.grid()\n",
+    "ax.set_ylabel('f [Hz]')\n",
+    "ax.set_ylim([30, 75]) # Hz\n",
+    "ax.set_xlabel('simulation time t [s]')\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step 3: Run Gasior and Gonzalez for precise frequency estimation\n",
+    "\n",
+    "Limit analysis to frequency range of interest. If automatic adaption to totally different frequency ranges\n",
+    "(e.g. 400Hz) would be necessary, we could switch here based on configuration or a lookup of the STFT bin\n",
+    "containing highest overall energy.\n",
+    "\n",
+    "As elaborated in the Gasior and Gonzalez Paper [1] the shape of the template function should match the expected peak shape.\n",
+    "Peak shape is determined by the STFT window function. As Gasior and Gonzalez note, a gaussian is a very good fit for a steep gaussian window."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "fd30a988dcb84bc0a29e74d3134167e6",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "HBox(children=(FloatProgress(value=0.0, max=5443.0), HTML(value='')))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "f_t = t\n",
+    "\n",
+    "n_f, n_t = Zxx.shape\n",
+    "# Frequency ROI\n",
+    "f_min, f_max = 30, 70 # Hz\n",
+    "# Indices of bins within ROI\n",
+    "bounds_f = slice(np.argmax(f > f_min), np.argmin(f < f_max))\n",
+    "\n",
+    "# Initialize output array\n",
+    "f_mean = np.zeros(Zxx.shape[1])\n",
+    "\n",
+    "# Iterate over STFT time slices\n",
+    "for le_t in tnrange(1, Zxx.shape[1] - 1):\n",
+    "    # Cut out ROI and compute magnitude of complex fourier coefficients\n",
+    "    frame_f = f[bounds_f]\n",
+    "    frame_Z = np.abs(Zxx[bounds_f, le_t])\n",
+    "\n",
+    "    # Template function. We use a gaussian here. This function needs to fit the window above.\n",
+    "    def gauss(x, *p):\n",
+    "        A, mu, sigma = p\n",
+    "        return A*np.exp(-(x-mu)**2/(2.*sigma**2))\n",
+    "\n",
+    "    # Calculate initial values for curve fitting\n",
+    "    f_start = frame_f[np.argmax(frame_Z)] # index of strongest bin index\n",
+    "    A_start = np.max(frame_Z) # strongest bin value\n",
+    "    p0 = [A_start, f_start, 1.]\n",
+    "    try:\n",
+    "        # Fit template to measurement data STFT ROI \n",
+    "        coeff, var = optimize.curve_fit(gauss, frame_f, frame_Z, p0=p0)\n",
+    "        _A, f_mean[le_t], _sigma, *_ = coeff # The measured frequency is the mean of the fitted gaussian\n",
+    "        \n",
+    "    except Exception as e:\n",
+    "        # Handle fit errors\n",
+    "        f_mean[le_t] = np.nan"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Produce a plot of measurement results\n",
+    "\n",
+    "Include measurements of mean, standard deviation and variance of measurement data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "1baa6cf9948b4faeb79ad81940e2b4a0",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(9, 5), sharex=True)\n",
+    "fig.tight_layout(pad=2.2, h_pad=0, w_pad=1)\n",
+    "\n",
+    "# Cut off invalid values at fringes\n",
+    "ax.plot(f_t[1:-2], f_mean[1:-2])\n",
+    "ax.set_ylabel('f [Hz]')\n",
+    "ax.grid()\n",
+    "\n",
+    "var = np.var(f_mean[~np.isnan(f_mean)][1:-1])\n",
+    "mean = np.mean(f_mean[~np.isnan(f_mean)][1:-1])\n",
+    "ax.text(0.5, 0.95, f'Run {run_id}', transform=ax.transAxes, ha='center', fontweight='bold', color='white', bbox=bbox)\n",
+    "ax.text(0.05, 0.95, f'μ={mean:.3g} Hz', transform=ax.transAxes, ha='left', color='white', bbox=bbox)\n",
+    "ax.text(0.05, 0.89, f'σ={np.sqrt(var) * 1e3:.3g} mHz', transform=ax.transAxes, ha='left', color='white', bbox=bbox)\n",
+    "ax.text(0.05, 0.83, f'σ²={var * 1e3:.3g} mHz²', transform=ax.transAxes, ha='left', color='white', bbox=bbox)\n",
+    "\n",
+    "# Indicated missing values\n",
+    "for i in np.where(np.isnan(f_mean))[0]:\n",
+    "    ax.axvspan(f_t[i], f_t[i+1], color='lightblue')\n",
+    "\n",
+    "formatter = matplotlib.ticker.FuncFormatter(lambda s, x: str(datetime.timedelta(seconds=s)))\n",
+    "ax.xaxis.set_major_formatter(formatter)\n",
+    "ax.set_xlabel('recording time t [hh:mm:ss]')\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "708dbcdd2292469398199a0f6054a09d",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "ename": "IndexError",
+     "evalue": "index 0 is out of bounds for axis 0 with size 0",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-18-8b77e38496af>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     56\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m \u001b[0;31m# Cut out first 10min of filtered data to give filters time to settle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m \u001b[0mrms_slice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfiltered2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf_t\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m60\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     59\u001b[0m \u001b[0mrms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msquare\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrms_slice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m \u001b[0max1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34mf'RMS (band-pass): {rms*1e3:.3f}mHz'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransform\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0max1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransAxes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'white'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbbox\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbbox\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'center'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mIndexError\u001b[0m: index 0 is out of bounds for axis 0 with size 0"
+     ]
+    }
+   ],
+   "source": [
+    "f_copy = np.copy(f_mean[1:-1])\n",
+    "f_copy[np.isnan(f_copy)] = np.mean(f_copy[~np.isnan(f_copy)])\n",
+    "b, a = signal.cheby2(7, 86, 100, 'low', output='ba', fs=1000)\n",
+    "filtered = signal.lfilter(b, a, f_copy)\n",
+    "\n",
+    "b2, a2 = signal.cheby2(3, 30, 1, 'high', output='ba', fs=1000)\n",
+    "filtered2 = signal.lfilter(b2, a2, filtered)\n",
+    "\n",
+    "fig, (ax2, ax1) = plt.subplots(2, figsize=(9,7))\n",
+    "ax1.plot(f_t[1:-1], f_copy, color='lightgray')\n",
+    "ax1.set_ylim([49.90, 50.10])\n",
+    "ax1.grid()\n",
+    "formatter = matplotlib.ticker.FuncFormatter(lambda s, x: str(datetime.timedelta(seconds=s)))\n",
+    "ax1.xaxis.set_major_formatter(formatter)\n",
+    "zoom_offx = 7000 # s\n",
+    "zoom_len = 300 # s\n",
+    "ax1.set_xlim([zoom_offx, zoom_offx + zoom_len])\n",
+    "\n",
+    "ax1.plot(f_t[1:-1], filtered, color='orange')\n",
+    "ax1r = ax1.twinx()\n",
+    "ax1r.plot(f_t[1:-1], filtered2, color='red')\n",
+    "ax1r.set_ylim([-0.015, 0.015])\n",
+    "ax1.set_title(f'Zoomed trace ({datetime.timedelta(seconds=zoom_len)})', pad=-20)\n",
+    "\n",
+    "\n",
+    "ax2.set_title(f'Run {last_run}')\n",
+    "ax2.plot(f_t[1:-1], f_copy, color='orange')\n",
+    "\n",
+    "ax2r = ax2.twinx()\n",
+    "ax2r.set_ylim([-0.1, 0.1])\n",
+    "ax2r.plot(f_t[1:-1], filtered2, color='red')\n",
+    "#ax2.plot(f_t[1:-1], filtered, color='orange', zorder=1)\n",
+    "ax2.set_ylim([49.90, 50.10])\n",
+    "ax2.set_xlim([0, f_t[-2]])\n",
+    "ax2.grid()\n",
+    "formatter = matplotlib.ticker.FuncFormatter(lambda s, x: str(datetime.timedelta(seconds=s)))\n",
+    "ax2.xaxis.set_major_formatter(formatter)\n",
+    "\n",
+    "ax2.legend(handles=[\n",
+    "    patches.Patch(color='lightgray', label='Raw frequency'),\n",
+    "    patches.Patch(color='orange', label='low-pass filtered'),\n",
+    "    patches.Patch(color='red', label='band-pass filtered')])\n",
+    "\n",
+    "#ax2r.spines['right'].set_color('red')\n",
+    "ax2r.yaxis.label.set_color('red')\n",
+    "#ax2r.tick_params(axis='y', colors='red')\n",
+    "\n",
+    "#ax1r.spines['right'].set_color('red')\n",
+    "ax1r.yaxis.label.set_color('red')\n",
+    "#ax1r.tick_params(axis='y', colors='red')\n",
+    "\n",
+    "ax1.set_ylabel('f [Hz]')\n",
+    "ax1r.set_ylabel('band-pass Δf [Hz]')\n",
+    "ax2.set_ylabel('f [Hz]')\n",
+    "ax2r.set_ylabel('band-pass Δf [Hz]')\n",
+    "\n",
+    "# Cut out first 10min of filtered data to give filters time to settle\n",
+    "rms_slice = filtered2[np.where(f_t[1:] > 10*60)[0][0]:]\n",
+    "rms = np.sqrt(np.mean(np.square(rms_slice)))\n",
+    "ax1.text(0.5, 0.1, f'RMS (band-pass): {rms*1e3:.3f}mHz', transform=ax1.transAxes, color='white', bbox=bbox, ha='center')\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chunk_size = 256\n",
+    "#\n",
+    "#with open('filtered_freq.bin', 'wb') as f:\n",
+    "#    for chunk in range(0, len(rms_slice), chunk_size):\n",
+    "#        out_data = rms_slice[chunk:chunk+chunk_size]\n",
+    "#        f.write(struct.pack(f'{len(out_data)}f',  *out_data))\n",
+    "#        \n",
+    "#with open('raw_freq.bin', 'wb') as f:\n",
+    "#    for chunk in range(0, len(f_copy), chunk_size):\n",
+    "#        out_data = f_copy[chunk:chunk+chunk_size]\n",
+    "#        f.write(struct.pack(f'{len(out_data)}f',  *out_data))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Number of samplepoints\n",
+    "N = len(data_not_nan)\n",
+    "# sample spacing\n",
+    "T = 1.0 / sampling_rate\n",
+    "x = np.linspace(0.0, N*T, N)\n",
+    "yf = scipy.fftpack.fft(data_not_nan * sig.blackman(N))\n",
+    "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
+    "\n",
+    "yf = 2.0/N * np.abs(yf[:N//2])\n",
+    "\n",
+    "average_from = lambda val, start, average_width: np.hstack([val[:start], [ np.mean(val[i:i+average_width]) for i in range(start, len(val), average_width) ]])\n",
+    "\n",
+    "average_width = 6\n",
+    "average_start = 20\n",
+    "yf = average_from(yf, average_start, average_width)\n",
+    "xf = average_from(xf, average_start, average_width)\n",
+    "yf = average_from(yf, 200, average_width)\n",
+    "xf = average_from(xf, 200, average_width)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(6, 3))\n",
+    "fig.tight_layout()\n",
+    "ax.loglog(xf, yf)\n",
+    "#ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
+    "ax.set_xlabel('f [Hz]')\n",
+    "ax.set_ylabel('Amplitude V [V]')\n",
+    "ax.grid()\n",
+    "ax.set_xlim([0.001, 500])\n",
+    "fig.subplots_adjust(bottom=0.2)\n",
+    "\n",
+    "for le_f in (50, 150, 250, 350, 450):\n",
+    "    ax.axvline(le_f, color=(1, 0.5, 0.5), zorder=-2)\n",
+    "ax.annotate('50 Hz', xy=(20, 1), xycoords='data', bbox=dict(fc='white', alpha=0.8, ec='none'))\n",
+    "font = {'family' : 'normal',\n",
+    "        'weight' : 'normal',\n",
+    "        'size'   : 10}\n",
+    "matplotlib.rc('font', **font)\n",
+    "fig.savefig('fig_out/mains_voltage_spectrum.eps')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Number of samplepoints\n",
+    "newcopy = np.copy(f_mean[1:-2])\n",
+    "\n",
+    "nans, x = nan_helper(newcopy)\n",
+    "newcopy[nans]= np.interp(x(nans), x(~nans), newcopy[~nans])\n",
+    "\n",
+    "N = len(newcopy)\n",
+    "# sample spacing\n",
+    "T = 1.0 / 10\n",
+    "x = np.linspace(0.0, N*T, N)\n",
+    "yf = scipy.fftpack.fft(newcopy * sig.blackman(N))\n",
+    "xf = np.linspace(0.0, 10/2, N//2)\n",
+    "\n",
+    "yf = 2.0/N * np.abs(yf[:N//2])\n",
+    "\n",
+    "average_from = lambda val, start, average_width: np.hstack([val[:start], [ np.mean(val[i:i+average_width]) for i in range(start, len(val), average_width) ]])\n",
+    "\n",
+    "average_width1, average_start1 = 3, 40\n",
+    "average_width2, average_start2 = 4, 100\n",
+    "yf = average_from(yf, average_start1, average_width1)\n",
+    "xf = average_from(xf, average_start1, average_width1)\n",
+    "yf = average_from(yf, average_start2, average_width2)\n",
+    "xf = average_from(xf, average_start2, average_width2)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.loglog(xf, yf)\n",
+    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
+    "ax.set_xlabel('T [s]')\n",
+    "ax.set_ylabel('Amplitude Δf [Hz]')\n",
+    "\n",
+    "for i, t in enumerate([60, 300, 450, 1200, 1800]):\n",
+    "    ax.axvline(1/t, color='red', alpha=0.5)\n",
+    "    ax.annotate(f'{t} s', xy=(1/t, 3e-5), xytext=(-15, 0), xycoords='data', textcoords='offset pixels', rotation=90)\n",
+    "#ax.text(1/60, 10,'60 s', ha='left')\n",
+    "ax.grid()\n",
+    "#ax.set_xlim([1/60000, 0.5])\n",
+    "#ax.set_ylim([5e-7, 2e-2])\n",
+    "#ax.plot(xf[1:], 2e-6/xf[1:])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(np.linspace(0, (len(f_mean)-3)/10, len(f_mean)-3) , f_mean[1:-2])\n",
+    "ax.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "\n",
+    "1. **Gasior, M. & Gonzalez, J.** Improving FFT frequency measurement resolution by parabolic and gaussian interpolation *CERN-AB-Note-2004-021, CERN-AB-Note-2004-021, 2004*"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/rocof_test_data.py

@@ -0,0 +1,174 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# # ROCOF test waveform library
+# 
+# This is a re-implementation of the ROCOF test waveforms described in https://zenodo.org/record/3559798
+# 
+# **This file is exported as a python module and loaded from other notebooks here, so please make sure to re-export when changing it.**
+
+# In[ ]:
+
+
+import math
+import itertools
+
+import numpy as np
+from scipy import signal
+from matplotlib import pyplot as plt
+
+
+# In[ ]:
+
+
+def sample_waveform(generator, duration:"s"=10, sampling_rate:"sp/s"=10000, frequency:"Hz"=50):
+    samples = int(duration*sampling_rate)
+    phases = np.linspace(0, 2*np.pi, 6, endpoint=False)
+    omega_t = np.linspace(phases, phases + 2*np.pi*duration*frequency, samples)
+    fundamental = np.sin(omega_t)
+    return generator(omega_t, fundamental, sampling_rate=sampling_rate, duration=duration, frequency=frequency).swapaxes(0, 1)
+
+
+# In[ ]:
+
+
+def gen_harmonics(amplitudes, phases=[]):
+    return lambda omega_t, fundamental, **_: fundamental + np.sum([
+                a*np.sin((p if p else 0) + i*omega_t)
+                   for i, (a, p) in enumerate(itertools.zip_longest(amplitudes, phases), start=2)
+    ], axis=0)
+
+def test_harmonics():
+    return gen_harmonics([0.02, 0.05, 0.01, 0.06, 0.005, 0.05, 0.005, 0.015, 0.005, 0.035, 0.005, 0.003])
+
+
+# In[ ]:
+
+
+def gen_interharmonic(amplitudes, ih=[], ih_phase=[]):
+    def gen(omega_t, fundamental, **_):
+        return fundamental + np.sum([
+            a*np.sin(omega_t * ih + (p if p else 0))
+            for a, ih, p in itertools.zip_longest(amplitudes, ih, ih_phase)
+        ], axis=0)
+    return gen
+
+def test_interharmonics():
+    return gen_interharmonic([0.1], [15.01401], [np.pi])
+
+
+# In[ ]:
+
+
+def gen_noise(amplitude=0.2, fmax:'Hz'=4.9e3, fmin:'Hz'=100, filter_order=6):
+    def gen(omega_t, fundamental, sampling_rate, **_):
+        noise = np.random.normal(0, amplitude, fundamental.shape)
+        b, a = signal.butter(filter_order,
+                             [fmin, min(fmax, sampling_rate//2-1)],
+                             btype='bandpass',
+                             fs=sampling_rate)
+        return fundamental + signal.lfilter(b, a, noise, axis=0)
+    return gen
+
+def test_noise():
+    return gen_noise()
+
+def test_noise_loud():
+    return gen_noise(amplitude=0.5, fmin=10)
+
+
+# In[406]:
+
+
+def gen_steps(size_amplitude=0.1, size_phase=0.1*np.pi, steps_per_sec=1):
+    def gen(omega_t, fundamental, duration, **_):
+        n = int(steps_per_sec * duration)
+        indices = np.random.randint(0, len(omega_t), n)
+        amplitudes = np.random.normal(1, size_amplitude, (n, 6))
+        phases = np.random.normal(0, size_phase, (n, 6))
+        amplitude = np.ones(omega_t.shape)
+        for start, end, a, p in zip(indices, indices[1:], amplitudes, phases):
+            omega_t[start:end] += p
+            amplitude[start:end] = a
+        return amplitude*np.sin(omega_t)
+    return gen
+
+def test_amplitude_steps():
+    return gen_steps(size_amplitude=0.4, size_phase=0)
+
+def test_phase_steps():
+    return gen_steps(size_amplitude=0, size_phase=0.1)
+
+def test_amplitude_and_phase_steps():
+    return gen_steps(size_amplitude=0.2, size_phase=0.07)
+
+
+# In[418]:
+
+
+def step_gen(shape, stdev, duration, steps_per_sec=1.0, mean=0.0):
+    samples, channels = shape
+    n = int(steps_per_sec * duration)
+    indices = np.random.randint(0, samples, n)
+    phases = np.random.normal(mean, stdev, (n, 6))
+    amplitude = np.ones((samples, channels))
+    out = np.zeros(shape)
+    for start, end, a in zip(indices, indices[1:], amplitude):
+        out[start:end] = a
+    return out
+
+def gen_chirp(fmin, fmax, period, dwell_time=1.0, amplitude=None, phase_steps=None):
+    def gen(omega_t, fundamental, sampling_rate, duration, **_):
+        samples = int(duration*sampling_rate)
+        phases = np.linspace(0, 2*np.pi, 6, endpoint=False)
+        
+        c = (fmax-fmin)/period
+        t = np.linspace(0, duration, samples)
+        
+        x = np.repeat(np.reshape(2*np.pi*fmin*t, (-1,1)), 6, axis=1)
+        data = (phases + x)[:int(sampling_rate*dwell_time)]
+        current_phase = 2*np.pi*fmin*dwell_time
+        direction = 'up'
+        
+        for idx in range(int(dwell_time*sampling_rate), samples, int(2*period*sampling_rate)):
+            t1 = np.linspace(0, period, int(period*sampling_rate))
+            t2 = np.linspace(0, period, int(period*sampling_rate))
+            chirp_phase = np.hstack((
+                2*np.pi*(c/2 * t1**2 + fmin * t1),
+                2*np.pi*(-c/2 * t2**2 + fmax * t2 - (c/2 * period**2 + fmin * period))
+            ))
+            chirp_phase = np.repeat(np.reshape(chirp_phase, (-1, 1)), 6, axis=1)
+            new = phases + chirp_phase + current_phase
+            current_phase = chirp_phase[-1]
+            data = np.vstack((data, new))
+            
+        data = data[:len(fundamental)]
+        
+        if phase_steps:
+            (step_amplitude, steps_per_sec) = phase_steps
+            steps = step_gen(data.shape, step_amplitude, duration, steps_per_sec)
+            data += steps
+            
+        if amplitude is None:
+            return np.sin(data)
+        else:
+            return fundamental + amplitude*np.sin(data)
+    return gen
+
+def test_close_interharmonics_and_flicker():
+    return gen_chirp(90.0, 150.0, 10, 1, amplitude=0.1)
+
+def test_off_frequency():
+#     return gen_chirp(48.0, 52.0, 0.25, 1)
+     return gen_chirp(48.0, 52.0, 10, 1)
+
+def test_sweep_phase_steps():
+    return gen_chirp(48.0, 52.0, 10, 1, phase_steps=(0.1, 1))
+#     return gen_chirp(48.0, 52.0, 0.25, 1, phase_steps=(0.1, 1))
+
+
+# In[ ]:
+
+
+all_tests = [test_harmonics, test_interharmonics, test_noise, test_noise_loud, test_amplitude_steps, test_phase_steps, test_amplitude_and_phase_steps, test_close_interharmonics_and_flicker, test_off_frequency, test_sweep_phase_steps]
+

notebooks/scratch.ipynb

@@ -0,0 +1,845 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import json\n",
+    "import csv\n",
+    "import re\n",
+    "import math\n",
+    "import struct\n",
+    "\n",
+    "import numpy as np\n",
+    "from matplotlib import pyplot as plt\n",
+    "import matplotlib\n",
+    "\n",
+    "import scipy.signal as sig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def read_freq_log(fn):\n",
+    "    with open(fn) as f:\n",
+    "        def parse_freq(f):\n",
+    "            try:\n",
+    "                return float(f)\n",
+    "            except:\n",
+    "                return 0\n",
+    "        freqs = np.trim_zeros(np.array([ parse_freq(line.split()[1]) for line in f.readlines() if re.match('\\d+: .*', line) ]))\n",
+    "        return freqs[np.nonzero(freqs)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "57f40afcd2214d0392a5fc7577843454",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(2, 2, figsize=(15, 9))\n",
+    "ax1, ax2, ax3, ax4 = axs.flatten()\n",
+    "\n",
+    "freqs_mod, freqs_clean, freqs_clean_gnd = read_freq_log('/mnt/c/Users/jaseg/shared/dsss_test.log'), read_freq_log('/mnt/c/Users/jaseg/shared/dsss_test_50hz_clean.log'), read_freq_log('/mnt/c/Users/jaseg/shared/dsss_test_50hz_clean_gndtest.log')\n",
+    "\n",
+    "ax1.plot(freqs_mod)\n",
+    "ax1.grid()\n",
+    "\n",
+    "ax2.plot(freqs_clean)\n",
+    "ax2.grid()\n",
+    "\n",
+    "ax4.plot(freqs_clean_gnd)\n",
+    "ax4.grid()\n",
+    "\n",
+    "w = 512\n",
+    "\n",
+    "ax3.psd(freqs_mod[:80000], w, 100/128 * 10)\n",
+    "ax3.psd(freqs_clean[:80000], w, 100/128 * 10)\n",
+    "ax3.psd(freqs_clean_gnd[:80000], w, 100/128 * 10)\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "8b2507e2a7a24129acddcdbb4356f8df",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(2, 2, figsize=(15, 9))\n",
+    "ax1, ax2, ax3, ax4 = axs.flatten()\n",
+    "\n",
+    "freqs_mod, freqs_clean = read_freq_log('data/meas_sig_audio_test.log'), read_freq_log('/mnt/c/Users/jaseg/shared/dsss_test_50hz_clean_improved.log')\n",
+    "\n",
+    "ax1.plot(freqs_mod)\n",
+    "ax1.grid()\n",
+    "\n",
+    "ax2.plot(freqs_clean)\n",
+    "ax2.grid()\n",
+    "\n",
+    "w = 512\n",
+    "\n",
+    "ax3.psd(freqs_mod[:80000], w, 100/128 * 10)\n",
+    "ax4.psd(freqs_clean[:80000], w, 100/128 * 10)\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open('data/dsss_test_demod_fixed_05.bin', 'wb') as f:\n",
+    "    for freq in read_freq_log('data/dsss_test_demod_fixed_05.log'):\n",
+    "        f.write(struct.pack('f', freq))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "d3a944613a184c44be006ef957770e31",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f49ad047130>]"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(read_freq_log('data/dsss_test_demod_fixed_03.log'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "5d366527c29840da9404ec7b1e1e0665",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(84250, 86000)"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(2, 1, figsize=(15, 6))\n",
+    "ax1, ax2 = axs.flatten()\n",
+    "\n",
+    "freqs_mod = read_freq_log('data/meas_sig_audio_test.log')\n",
+    "\n",
+    "with open('data/meas_sig_audio_test.bin', 'wb') as f:\n",
+    "    for freq in freqs_mod:\n",
+    "        f.write(struct.pack('f', freq))\n",
+    "        \n",
+    "with open('data/ref_sig_audio_test.bin', 'rb') as f:\n",
+    "    freqs_ref = np.array(list(struct.iter_unpack('f', f.read())))\n",
+    "\n",
+    "ax1.plot(freqs_mod)\n",
+    "ax1.set_title('measured')\n",
+    "ax1.grid()\n",
+    "ax2.plot(freqs_ref)\n",
+    "ax2.set_title('reference')\n",
+    "ax2.grid()\n",
+    "\n",
+    "ax1.set_xlim([84250+47, 86000+47])\n",
+    "ax2.set_xlim([84250, 86000])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def read_raw_log(fn):\n",
+    "    with open(fn) as f:\n",
+    "        vals = np.array([ int(x, 16) for line in f for x in line.partition(':')[2].split() ])\n",
+    "        return vals"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "bc4efa3809dd423482f1ef34974192c0",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "<ipython-input-19-55f36f700399>:6: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
+      "  fig.tight_layout()\n"
+     ]
+    }
+   ],
+   "source": [
+    "# We see artifacts of the 128sp processing window in the analog readings if we process a buffer immediately after capture. We can reduce these artifacts by deferring the sampling a few milliseconds into the capture period.\n",
+    "# The reason for this is presumably a suboptimal power layout on the cheap f407 devboard leading to CPU load changes dumping noise into our ADC supply.\n",
+    "# In time domain plots we can see frequent high spikes in ADC counts that would be in accordance with this conjecture.\n",
+    "\n",
+    "fig, axs = plt.subplots(2, 2, figsize=(15, 9), sharey='row', gridspec_kw={'hspace': 0.2, 'wspace': 0.05})\n",
+    "fig.tight_layout()\n",
+    "ax1, ax2, ax3, ax4 = axs.flatten()\n",
+    "\n",
+    "raw_left, raw_right = read_raw_log('data/rawlog_silence_clean.log'), read_raw_log('data/rawlog_silence_clean3.log')\n",
+    "raw_left = raw_left[26000:-10000].astype(float)\n",
+    "\n",
+    "raw_right = raw_right[26000:]\n",
+    "raw_right = raw_right[:len(raw_left)].astype(float)\n",
+    "\n",
+    "raw_left -= np.mean(raw_left)\n",
+    "raw_right -= np.mean(raw_right)\n",
+    "\n",
+    "ax1.set_title('Immediate processing')\n",
+    "ax1.plot(raw_left)\n",
+    "ax1.grid()\n",
+    "for x in range(0, len(raw_left), 128):\n",
+    "    ax1.axvline(x, color='red', alpha=0.3)\n",
+    "\n",
+    "ax2.set_title('Deferred processing')\n",
+    "ax2.plot(raw_right)\n",
+    "ax2.grid()\n",
+    "for x in range(0, len(raw_right), 128):\n",
+    "    ax2.axvline(x, color='red', alpha=0.3)\n",
+    "\n",
+    "ax1.set_xlim([0, 1000])\n",
+    "ax1.set_ylim([-200, 200])\n",
+    "ax2.set_xlim([0, 1000])\n",
+    "ax2.set_ylim([-200, 200])\n",
+    "ax1.set_xlabel('t [ms]')\n",
+    "ax2.set_xlabel('t [ms]')\n",
+    "ax1.set_ylabel('ADC reading [counts]')\n",
+    "\n",
+    "w = 2048\n",
+    "\n",
+    "ax3.psd(raw_left, w, 1e3)\n",
+    "ax4.psd(raw_right, w, 1e3)\n",
+    "ax3.set_ylim([-10, 26])\n",
+    "ax4.set_ylim([-10, 26])\n",
+    "ax4.set_ylabel(None)\n",
+    "None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "291774359d674902aad182268ec9c469",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(12, 6))\n",
+    "\n",
+    "raw_silence = read_raw_log('data/rawlog_silence_clean.log')\n",
+    "raw_silence2 = read_raw_log('data/rawlog_silence_clean3.log')\n",
+    "\n",
+    "raw_silence = raw_silence.reshape([-1, 128])\n",
+    "le_mean = raw_silence.mean(axis=0)\n",
+    "ax.plot(le_mean - np.mean(le_mean))\n",
+    "\n",
+    "raw_silence2 = raw_silence2.reshape([-1, 128])\n",
+    "le_mean2 = raw_silence2.mean(axis=0)\n",
+    "ax.plot(le_mean2 - np.mean(le_mean2))\n",
+    "ax.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "<ipython-input-40-132a47f1202f>:1: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
+      "  fig, axs = plt.subplots(4, 1, figsize=(15, 9), sharex=True)\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2740bc857e6c4296b9ca74ada34fbb1d",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(4, 1, figsize=(15, 9), sharex=True)\n",
+    "ax1, ax2, ax3, ax4 = axs.flatten()\n",
+    "\n",
+    "#with open('data/meas_sig_audio_test_processed.log') as f:\n",
+    "with open('data/meas_sig_audio_test_fixed_03.log') as f:\n",
+    "    lines = f.readlines()\n",
+    "    data = np.array([ [float(x) for x in line.split(': ')[1].split()] for line in lines if not line.startswith('GROUP:') ])\n",
+    "    groups = [ int(line.split(' ')[2]) for line in lines if line.startswith('GROUP:') ]\n",
+    "\n",
+    "ax1.plot(data[:,0])\n",
+    "ax1.grid()\n",
+    "ax1.set_xlim([4000, 16000])\n",
+    "ax1.set_ylim([-0.02, 0.1])\n",
+    "\n",
+    "ax2.plot(data[:,1:-2:2])\n",
+    "ax2.grid()\n",
+    "ax2.set_ylim([-0.6, 0.6])\n",
+    "\n",
+    "ax3.plot(data[:,2:-2:2])\n",
+    "ax3.grid()\n",
+    "\n",
+    "ax4.plot(data[:,-2:])\n",
+    "ax4.grid()\n",
+    "\n",
+    "for x in groups:\n",
+    "    ax4.axvline(x, color='red', alpha=0.4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.lines.Line2D at 0x7f497186d6d0>"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ax4.axvline(12433)\n",
+    "ax4.axvline(12164)\n",
+    "ax4.axvline(12475)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "cff56db4807048cda06ae8b15b0c6344",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(4, 1, figsize=(15, 9), sharex=True)\n",
+    "ax1, ax2, ax3, ax4 = axs.flatten()\n",
+    "\n",
+    "with open('data/ref_sig_audio_test_processed.log') as f:\n",
+    "    lines = f.readlines()\n",
+    "    data = np.array([ [float(x) for x in line.split(': ')[1].split()] for line in lines if not line.startswith('GROUP:') ])\n",
+    "    groups = [ int(line.split(': ')[1]) for line in lines if line.startswith('GROUP:') ]\n",
+    "\n",
+    "ax1.plot(data[:,0])\n",
+    "ax1.grid()\n",
+    "ax1.set_xlim([82000, 95000])\n",
+    "ax1.set_ylim([-0.02, 0.1])\n",
+    "\n",
+    "ax2.plot(data[:,1:-2:2])\n",
+    "ax2.grid()\n",
+    "ax2.set_ylim([-0.6, 0.6])\n",
+    "\n",
+    "ax3.plot(data[:,2:-2:2])\n",
+    "ax3.grid()\n",
+    "\n",
+    "ax4.plot(data[:,-2:])\n",
+    "ax4.grid()\n",
+    "\n",
+    "for x in groups:\n",
+    "    ax4.axvline(x, color='red', alpha=0.4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[516, 518, 4402, 4404, 5537, 7238, 12585, 17497, 17724, 34074, 34076, 41628, 44677, 46287, 49371, 49837, 53877, 54554, 56666, 56949, 60923, 67313, 67744, 67746, 68392, 79601, 84707, 84709, 84711, 85017, 85019, 85021, 85327, 85329, 85637, 85947, 85949, 85951, 86257, 86259, 86261, 86567, 86569, 86571, 86877, 86879, 86881, 87187, 87189, 87191, 87498, 87500, 87807, 87809, 87811, 88117, 88119, 88121, 88427, 88429, 88431, 88488, 88737, 88739, 88741, 89047, 89049, 89051, 89357, 89359, 89361, 89668, 89670, 89730, 89978, 89980, 90287, 90289, 90291, 90598, 90600, 90602, 90907, 90909, 90911, 91217, 91219, 91221, 91527, 91529, 91531, 91837, 91839, 91841, 92148, 92150, 92458, 92460, 92768, 92770, 93078, 93080, 93388, 93390, 93392, 93698, 93700, 93702, 94008, 94010, 94318, 94320]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(groups)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "<ipython-input-79-e66d1dcc2be5>:1: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
+      "  fig, ax = plt.subplots(figsize=(9, 5))\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "48b1d8b994594af79c3dca2bf9a6fb41",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(9, 5))\n",
+    "\n",
+    "raw_c = read_raw_log('/mnt/c/Users/jaseg/shared/rawlog_test_c.log')\n",
+    "\n",
+    "ax.plot(raw_c[1000:2000])\n",
+    "ax.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "<ipython-input-25-f95a3be8874f>:1: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
+      "  fig, ax = plt.subplots()\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "62a620e3551e46c38fb0d0e017b8e357",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f731d79f2b0>]"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot([797, 813, 869, 971, 1128, 1298, 1461, 1609, 1750, 1826, 1881, 1860, 1789, 1695, 1552, 1360, 1209, 1048, 921, 832, 803, 812, 870, 972, 1125, 1284, 1461, 1618, 1757, 1834, 1835, 1861, 1795, 1685, 1545, 1383, 1217, 1046, 908, 832,\n",
+    "  800, 815, 864, 993, 1084, 1296, 1453, 1613, 1746, 1833, 1875, 1859, 1794, 1693, 1542, 1352, 1211, 1049, 916, 833, 800, 810, 875, 992, 1144, 1300, 1447, 1606, 1735, 1836, 1846, 1869, 1811, 1701, 1557, 1375, 1208, 1060, 936, 836, 805,\n",
+    "  796, 877, 986, 1134, 1288, 1458, 1613, 1737, 1847, 1865, 1867, 1792, 1688, 1556, 1373, 1209, 1049, 928, 827, 792, 821, 869, 972, 1122, 1295, 1457, 1595, 1745, 1847, 1877, 1867, 1789, 1683, 1539, 1378, 1210, 1047, 917, 833, 817, 821,\n",
+    "  869, 977, 1128, 1299, 1458, 1630, 1711, 1833, 1833, 1869, 1800, 1715, 1545, 1375, 1217, 1060, 917, 841, 812, 826, 878, 985, 1128, 1280, 1452, 1612, 1739, 1827, 1892, 1864, 1793, 1700, 1547, 1375, 1212, 1054, 921, 829, 795, 809, 869,\n",
+    "  990, 1077, 1284, 1459, 1616, 1753, 1864, 1874, 1865, 1807, 1696, 1543, 1390, 1274, 1047, 926, 831, 804, 806, 872, 987, 1100, 1278, 1447, 1604, 1743, 1831, 1879, 1849, 1780, 1660, 1540, 1389, 1176, 1064, 928, 828, 812, 809, 875, 983,\n",
+    "  1128, 1285, 1456, 1611, 1739, 1889, 1879, 1879, 1793, 1680, 1546, 1381, 1215, 1074, 926, 842, 794, 857, 859, 978, 1123, 1290, 1427, 1607, 1737, 1835, 1882, 1861, 1815, 1694, 1532, 1375, 1202, 1050, 928, 822, 802, 810, 854, 990, 1119,\n",
+    "  1292, 1455, 1619, 1738, 1827, 1871, 1847, 1800, 1693, 1551, 1379])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "fb0ad935348d4b3dab1c3548b9cfd628",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(0, 64)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "a = np.array([-00.000732, -00.000352, -00.000666, -00.000202, -00.000706, -00.000006, -00.000597, -00.002039, 000.050663, -00.644566, 004.456614, -16.817095, 034.654587, -39.021217, 024.007816, -08.070650, 001.478795, -00.150260, 000.006110, -00.002328, -00.002322, -00.002426, -00.002177, -00.002452, -00.002333, -00.002438, -00.002342, -00.002396, -00.001979, -00.003049, -00.001720, -00.002686, -00.002168, -00.002507, -00.001868, -00.002899, -00.002017, -00.001952, -00.003255, -00.001080, -00.003335, -00.001575, -00.002704, -00.001872, -00.002735, -00.001983, -00.002191, -00.002478, -00.002155, -00.002203, -00.002328, -00.002206, -00.002443, -00.001770, -00.002718, -00.002004, -00.002378, -00.002112, -00.002122, -00.002691, -00.001679, -00.002690, -00.001946, -00.002232])\n",
+    "b = np.array([-00.002734, -00.001325, -00.002220, -00.003693, -00.004907, -00.006454, -00.007737, 000.004823, -00.363143, 004.688968, -33.795303, 130.992630, -274.092651, 309.377991, -188.427826, 061.912941, -10.974002, 001.053608, -00.048927, 000.007710, 000.007010, 000.006493, 000.007234, 000.006725, 000.006938, 000.006694, 000.006356, 000.006173, 000.006333, 000.005684, 000.005697, 000.005575, 000.005101, 000.005693, 000.004319, 000.005344, 000.004673, 000.003566, 000.006213, 000.002719, 000.004850, 000.003755, 000.004243, 000.003419, 000.003960, 000.003498, 000.003297, 000.003877, 000.002836, 000.003487, 000.003144, 000.002824, 000.003355, 000.002528, 000.002975, 000.003012, 000.002137, 000.003112, 000.002416, 000.002512, 000.002084, 000.003008, 000.001837, 000.002351])\n",
+    "ax.plot([3.906250*i for i in range(len(a))], np.sqrt(a**2 + b**2))\n",
+    "a2 = ax.twiny()\n",
+    "a2.set_xlim([0, len(a)])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "d4024377df494eac935fd487026edc8b",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f2eb410f280>]"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "d = [50.000839,50.000839,50.000832,50.000824,50.000839,50.000832,50.000839,50.000824,50.000847,50.000824,50.000824,50.000839,50.000832,50.000839,50.000824,50.000824,50.000839,50.000824,50.000824,50.000835,50.000816,50.000832,50.000847,50.000832,50.000835,50.000824,50.000824,50.000832,50.000832,50.000843,50.000824,50.000832,50.000832,50.000832,50.000828,50.000832,50.000832,50.000824,50.000816,50.000835,50.000843,50.000824,50.000824,50.000832,50.000832,50.000847,50.000824,50.000824,50.000824,50.000835,50.000835,50.000851,50.000824,50.000824,50.000832,50.000828,50.000828,50.000824,50.000832,50.000835,50.000835,50.000832,50.000847,50.000824,50.000832,50.000839,50.000839,50.000824,50.000832,50.000832,50.000832,50.000835,50.000816,50.000820,50.000824,50.000832,50.000824,50.000832,50.000835,50.000832,50.000816,50.000820,50.000839,50.000839,50.000824,50.000839,50.000820,50.000820,50.000839,50.000832,50.000835,50.000828,50.000824,50.000839,50.000839,50.000839,50.000816,50.000832,50.000824,50.000832,50.000832,50.000839,50.000824,50.000832,50.000828,50.000832,50.000828,50.000835,50.000832,50.000843,50.000839,50.000820,50.000832,50.000835,50.000824,50.000824,50.000828,50.000820,50.000820,50.000828,50.000832,50.000832,50.000828,50.000835,50.000839,50.000820,50.000832,50.000832,50.000824,50.000832,50.000832,50.000839,50.000839,50.000816,50.000828,50.000832,50.000839,50.000824,50.000824,50.000824,50.000835,50.000824,50.000832,50.000839,50.000835,50.000832,50.000828,50.000835,50.000828,50.000828,50.000824,50.000824,50.000839,50.000832,50.000824,50.000832,50.000832,50.000820,50.000851,50.000824,50.000824,50.000839,50.000824,50.000839,50.000832,50.000835,50.000820,50.000832,50.000839,50.000832,50.000832,50.000824,50.000832,50.000824,50.000832,50.000839,50.000839,50.000832,50.000816,50.000835,50.000854,50.000824,50.000816,50.000832,50.000832,50.000835,50.000816,50.000832,50.000824,50.000832,50.000832,50.000832,50.000824,50.000832,50.000824,50.000835,50.000832,50.000835,50.000832,50.000832,50.000828,50.000839,50.000824,50.000839,50.000824,50.000824,50.000839,50.000816,50.000839,50.000816,50.000832,50.000839,50.000839,50.000832,50.000824,50.000832,50.000820,50.000824,50.000835,50.000824,50.000835,50.000832,50.000824,50.000824,50.000820,50.000839,50.000816,50.000832,50.000832,50.000832,50.000824,50.000847,50.000824,50.000839]\n",
+    "\n",
+    "ax.plot(d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open('impl_test_out.json') as f:\n",
+    "    impl_measurements = json.load(f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "dd23cf23221e4e14aaafdd58bb9416d9",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(len(impl_measurements), figsize=(8, 20), sharex=True)\n",
+    "fig.tight_layout()\n",
+    "axs = axs.flatten()\n",
+    "\n",
+    "for (label, data), ax in zip(impl_measurements.items(), axs):\n",
+    "    ax.set_title(label)\n",
+    "    ax.plot(data[1:-1])\n",
+    "    mean = np.mean(data[1:-1])\n",
+    "    rms = np.sqrt(np.mean(np.square(data[1:-1] - mean)))\n",
+    "    ax.text(0.2, 0.2, f'mean={mean:.3}Hz, rms={rms*1e3:.3}mHz', ha='center', va='center', transform=ax.transAxes,\n",
+    "            bbox=dict(boxstyle=\"square\", ec=(0,0,0,0), fc=(1,1,1,0.8)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 2.35232554e-18,  4.70465108e-18,  2.35232554e-18,\n",
+       "         1.00000000e+00, -1.97549493e+00,  9.75650918e-01],\n",
+       "       [ 1.00000000e+00,  2.00000000e+00,  1.00000000e+00,\n",
+       "         1.00000000e+00, -1.97916324e+00,  9.79319515e-01],\n",
+       "       [ 1.00000000e+00,  2.00000000e+00,  1.00000000e+00,\n",
+       "         1.00000000e+00, -1.98597735e+00,  9.86134166e-01],\n",
+       "       [ 1.00000000e+00,  2.00000000e+00,  1.00000000e+00,\n",
+       "         1.00000000e+00, -1.99495144e+00,  9.95108965e-01]])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sig.butter(8, 20e-3, output='sos', fs=10.0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "655ce5c77d2a4047905245df39a095b0",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f4609ce6a90>]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot([0-0.00012937261, 0-0.00022784119 , 0-0.00039295876 , 0-0.00066361829 , 00-0.0010971602 , 00-0.0017754816 ,\n",
+    "    00-0.0028116399 , 00-0.0043560231 , 00-0.0066005666 , 00-0.0097788338 , 000-0.014159188 , 000-0.020027947 ,\n",
+    "    000-0.027659611 , 000-0.037272236 , 000-0.048968014 , 0000-0.06266222 , 0000-0.07800759 , 000-0.094325546 ,\n",
+    "    0000-0.11055938 , 0000-0.12526666 , 0000-0.13666715 , 0000-0.14275811 , 0000-0.14149973 , 00000-0.1310612 ,\n",
+    "    0000-0.11010384 , 000-0.078063987 , 000-0.035389599 , 00000.016317957 , 00000.074297836 , 000000.13478363 ,\n",
+    "    000000.19331697 , 000000.24519242 , 000000.28597909 , 000000.31204596 , 000000.32101141 , 000000.31204596 ,\n",
+    "    000000.28597909 , 000000.24519242 , 000000.19331697 , 000000.13478363 , 00000.074297836 , 00000.016317957 ,\n",
+    "    000-0.035389599 , 000-0.078063987 , 0000-0.11010384 , 00000-0.1310612 , 0000-0.14149973 , 0000-0.14275811 ,\n",
+    "    0000-0.13666715 , 0000-0.12526666 , 0000-0.11055938 , 000-0.094325546 , 0000-0.07800759 , 0000-0.06266222 ,\n",
+    "    000-0.048968014 , 000-0.037272236 , 000-0.027659611 , 000-0.020027947 , 000-0.014159188 , 00-0.0097788338 ,\n",
+    "    00-0.0066005666 , 00-0.0043560231 , 00-0.0028116399 , 00-0.0017754816 , 00-0.0010971602 , 0-0.00066361829 ,\n",
+    "    0-0.00039295876 , 0-0.00022784119 , 0-0.00012937261 ])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data = np.genfromtxt('/tmp/foo.csv', delimiter=',')[1000:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "7c771472882e4ceeb8aeddfa5c08ca17",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(2, figsize=(15, 9), sharex=True)\n",
+    "axs = axs.flatten()\n",
+    "axs[0].set_title('corr')\n",
+    "axs[1].set_title('cwt')\n",
+    "#axs[2].set_title('iir')\n",
+    "\n",
+    "axs[0].plot(data[:,0], label='corr')\n",
+    "axs[1].plot(data[:,1], label='cwt')\n",
+    "axs[0].plot(data[:,2], label='avg')\n",
+    "axs[1].plot(data[:,2], label='avg')\n",
+    "\n",
+    "for ax in axs:\n",
+    "    ax.legend()\n",
+    "    ax.grid()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/signal_gen.ipynb

@@ -0,0 +1,298 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import struct\n",
+    "import random\n",
+    "import itertools\n",
+    "import datetime\n",
+    "import multiprocessing\n",
+    "from collections import defaultdict\n",
+    "import json\n",
+    "\n",
+    "from matplotlib import pyplot as plt\n",
+    "import matplotlib\n",
+    "import numpy as np\n",
+    "from scipy import signal as sig\n",
+    "from scipy import fftpack as fftpack\n",
+    "import ipywidgets\n",
+    "\n",
+    "import pydub\n",
+    "\n",
+    "from tqdm.notebook import tqdm\n",
+    "import colorednoise\n",
+    "\n",
+    "np.set_printoptions(linewidth=240)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# From https://github.com/mubeta06/python/blob/master/signal_processing/sp/gold.py\n",
+    "preferred_pairs = {5:[[2],[1,2,3]], 6:[[5],[1,4,5]], 7:[[4],[4,5,6]],\n",
+    "                        8:[[1,2,3,6,7],[1,2,7]], 9:[[5],[3,5,6]], \n",
+    "                        10:[[2,5,9],[3,4,6,8,9]], 11:[[9],[3,6,9]]}\n",
+    "\n",
+    "def gen_gold(seq1, seq2):\n",
+    "    gold = [seq1, seq2]\n",
+    "    for shift in range(len(seq1)):\n",
+    "        gold.append(seq1 ^ np.roll(seq2, -shift))\n",
+    "    return gold\n",
+    "\n",
+    "def gold(n):\n",
+    "    n = int(n)\n",
+    "    if not n in preferred_pairs:\n",
+    "        raise KeyError('preferred pairs for %s bits unknown' % str(n))\n",
+    "    t0, t1 = preferred_pairs[n]\n",
+    "    (seq0, _st0), (seq1, _st1) = sig.max_len_seq(n, taps=t0), sig.max_len_seq(n, taps=t1)\n",
+    "    return gen_gold(seq0, seq1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def modulate(data, nbits=5, pad=True):\n",
+    "    # 0, 1 -> -1, 1\n",
+    "    mask = np.array(gold(nbits))*2 - 1\n",
+    "    \n",
+    "    sel = mask[data>>1]\n",
+    "    data_lsb_centered = ((data&1)*2 - 1)\n",
+    "\n",
+    "    signal = (np.multiply(sel, np.tile(data_lsb_centered, (2**nbits-1, 1)).T).flatten() + 1) // 2\n",
+    "    if pad:\n",
+    "        return np.hstack([ np.zeros(len(mask)), signal, np.zeros(len(mask)) ])\n",
+    "    else:\n",
+    "        return signal"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def generate_noisy_signal(\n",
+    "        test_duration=32,\n",
+    "        test_nbits=5,\n",
+    "        test_decimation=10,\n",
+    "        test_signal_amplitude=200e-3,\n",
+    "        noise_level=10e-3):\n",
+    "\n",
+    "    #test_data = np.random.RandomState(seed=0).randint(0, 2 * (2**test_nbits), test_duration)\n",
+    "    #test_data = np.array([0, 1, 2, 3] * 50)\n",
+    "    test_data = np.array(range(test_duration))\n",
+    "    signal = np.repeat(modulate(test_data, test_nbits, pad=False) * 2.0 - 1, test_decimation) * test_signal_amplitude\n",
+    "    noise = colorednoise.powerlaw_psd_gaussian(1, len(signal)*2) * noise_level\n",
+    "    noise[-int(1.5*len(signal)):][:len(signal)] += signal\n",
+    "\n",
+    "    return noise+50\n",
+    "    #with open(f'mains_sim_signals/dsss_test_noisy_padded.bin', 'wb') as f:\n",
+    "    #    for e in noise:\n",
+    "    #        f.write(struct.pack('<f', e))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "c778037402024206b195a27591dc0b40",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f2ab8cabca0>]"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(generate_noisy_signal())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open('data/ref_sig_audio_test3.bin', 'wb') as f:\n",
+    "    for x in generate_noisy_signal():\n",
+    "        f.write(struct.pack('f', x))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def synthesize_sine(freqs, freqs_sampling_rate=10.0, output_sampling_rate=44100):\n",
+    "    duration = len(freqs) / freqs_sampling_rate # seconds\n",
+    "    afreq_out = np.interp(np.linspace(0, duration, int(duration*output_sampling_rate)), np.linspace(0, duration, len(freqs)), freqs)\n",
+    "    return np.sin(np.cumsum(2*np.pi * afreq_out / output_sampling_rate))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "test_sig = synthesize_sine(generate_noisy_signal())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "5171d9dbbe5048e2b32c3cf7f7d03744",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f2a90476bb0>]"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(test_sig[:44100])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def save_signal_flac(filename, signal, sampling_rate=44100):\n",
+    "    signal -= np.min(signal)\n",
+    "    signal /= np.max(signal)\n",
+    "    signal -= 0.5\n",
+    "    signal *= 2**16 - 1\n",
+    "    le_bytes = signal.astype(np.int16).tobytes()\n",
+    "    seg = pydub.AudioSegment(data=le_bytes, sample_width=2, frame_rate=sampling_rate, channels=1)\n",
+    "    seg.export(filename, format='flac')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "save_signal_flac('synth_sig_test_0123_02.flac', synthesize_sine(generate_noisy_signal(), freqs_sampling_rate=10.0 * 100/128, output_sampling_rate=44100))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def emulate_adc_signal(adc_bits=12, adc_offset=0.4, adc_amplitude=0.25, freq_sampling_rate=10.0, output_sampling_rate=1000, **kwargs):\n",
+    "    signal = synthesize_sine(generate_noisy_signal(), freq_sampling_rate, output_sampling_rate)\n",
+    "    signal = signal*adc_amplitude + adc_offset\n",
+    "    smin, smax = np.min(signal), np.max(signal)\n",
+    "    if smin < 0.0 or smax > 1.0:\n",
+    "        raise UserWarning('Amplitude or offset too large: Signal out of bounds with min/max [{smin}, {smax}] of ADC range')\n",
+    "    signal *= 2**adc_bits -1\n",
+    "    return signal"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def save_adc_signal(fn, signal, dtype=np.uint16):\n",
+    "    with open(fn, 'wb') as f:\n",
+    "        f.write(signal.astype(dtype).tobytes())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "save_adc_signal('emulated_adc_readings_01.bin', emulate_adc_signal(freq_sampling_rate=10.0 * 100/128))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "labenv",
+   "language": "python",
+   "name": "labenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}