{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampling_rate = 10 # sp/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#colorednoise.powerlaw_psd_gaussian(1, int(1e4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.matshow(gold(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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'))"
   ]
  }
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