thesis: Add freq measurement notebook
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jaseg
parent
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commit
e104e5d2dc
9 changed files with 4650 additions and 9140 deletions
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Grid frequency estimation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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@ -30,13 +37,23 @@
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"%matplotlib widget"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Step 1: Setup\n",
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"### Load data series information from sqlite capture file\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"db = sqlite3.connect('data/waveform-raspi-2-2.sqlite3')"
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"db = sqlite3.connect('data/waveform-raspi-ocxo-2.sqlite3')"
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]
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},
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{
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@ -48,7 +65,9 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Run 000: 2020-03-25 16:07:36 - 2020-03-26 00:15:13 ( 8:07:37.266, 29261120sp)\n"
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"Run 000: 2020-04-01 14:00:25 - 2020-04-01 15:09:31 ( 1:09:05.846, 4197664sp)\n",
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"Run 001: 2020-04-02 11:56:41 - 2020-04-02 11:57:59 ( 0:01:18.544, 79552sp)\n",
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"Run 002: 2020-04-02 12:03:51 - 2020-04-02 12:12:54 ( 0:09:03.033, 549792sp)\n"
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]
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}
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],
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@ -57,8 +76,16 @@
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" foo = lambda x: datetime.datetime.fromtimestamp(x/1000)\n",
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" start, end = foo(start), foo(end)\n",
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" 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",
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"last_run, n_records = run_id, count\n",
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"sampling_rate = 1000.0"
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"last_run, n_records = run_id, count"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Setup analog parameters\n",
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"\n",
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"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."
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]
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},
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{
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@ -67,9 +94,11 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"sampling_rate = 1000.0 * 48.6 / 48\n",
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"\n",
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"par = lambda *rs: 1/sum(1/r for r in rs) # resistor parallel calculation\n",
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"\n",
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"# FIXME: These are for the first prototype only!\n",
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"# Note: These are for the first prototype only!\n",
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"vmeas_source_impedance = 330e3\n",
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"vmeas_source_scale = 0.5\n",
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"\n",
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@ -92,20 +121,29 @@
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"adc_count_to_vmeas = lambda x: (x*adc_val_to_voltage_factor - v0) / (v100-v0) * 100"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Load run data from sqlite3 capture file\n",
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"\n",
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"Load measurement data for the selected run and assemble a numpy array containing one continuous trace. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "582c4360e293466e9baed5bc66a47883",
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"model_id": "38970a137bed494d8c28c270471c73df",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"HBox(children=(FloatProgress(value=0.0, max=914410.0), HTML(value='')))"
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"HBox(children=(FloatProgress(value=0.0, max=17181.0), HTML(value='')))"
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]
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},
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"metadata": {},
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@ -115,7 +153,8 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n"
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"\n",
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"RMS voltage: 228.5564548966498\n"
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]
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}
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],
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@ -145,39 +184,44 @@
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" # nans[:] = np.nan\n",
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" # data = np.append(data, nans) FIXME\n",
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" \n",
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"data = (data * adc_val_to_voltage_factor - v0) / (v100-v0) * 100"
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"data = (data * adc_val_to_voltage_factor - v0) / (v100-v0) * 100\n",
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"\n",
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"# https://stackoverflow.com/questions/6518811/interpolate-nan-values-in-a-numpy-array\n",
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"nan_helper = lambda y: (np.isnan(y), lambda z: z.nonzero()[0])\n",
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"\n",
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"# data rarely may contain NaNs where the capture script failed to read and acknowledge capture buffers from the sensor board fast enough.\n",
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"# For RMS calculation and overall FFT fill these NaNs with interpolated values from their neighbors.\n",
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"data_not_nan = np.copy(data)\n",
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"nans, x = nan_helper(data)\n",
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"data_not_nan[nans]= np.interp(x(nans), x(~nans), data[~nans])\n",
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"\n",
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"print('RMS voltage:', np.sqrt(np.mean(np.square(data_not_nan))))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Show a preview of loaded data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"execution_count": 33,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"227.0922848236977"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"data_not_nan = data[~np.isnan(data)]\n",
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"np.sqrt(np.mean(np.square(data_not_nan)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"<ipython-input-33-4419e570bd12>: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",
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" fig, (top, bottom) = plt.subplots(2, figsize=(9,6))\n"
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]
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "ecf3e3e261c54d87b169c1eb391a67f9",
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"model_id": "6faa0da0b6b64d0094b9b683e5f2c434",
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"version_major": 2,
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"version_minor": 0
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},
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@ -191,7 +235,7 @@
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],
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"source": [
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"fig, (top, bottom) = plt.subplots(2, figsize=(9,6))\n",
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"fig.tight_layout(pad=3, h_pad=0.1)\n",
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"fig.tight_layout(pad=3, h_pad=1.8)\n",
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"\n",
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"range_start, range_len = -300, 60 # [s]\n",
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"\n",
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@ -205,68 +249,85 @@
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"peak = np.max(np.abs(data_not_nan - mean))\n",
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"top.axhline(mean, color='red')\n",
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"bbox = {'facecolor': 'black', 'alpha': 0.8, 'pad': 2}\n",
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"top.text(0, mean, f'mean: {mean:.3f}', color='white', bbox=bbox)\n",
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"top.text(0.02, 0.5, f'mean: {mean:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='left', va='center')\n",
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"top.text(0.98, 0.2, f'V_RMS: {rms:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='right')\n",
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"top.text(0.98, 0.1, f'V_Pk: {peak:.3f}', transform=top.transAxes, color='white', bbox=bbox, ha='right')\n",
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"top.text(0.5, 0.9, f'Run {run_id}', transform=top.transAxes, color='white', bbox=bbox, ha='center', fontweight='bold')\n",
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"\n",
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"bottom.grid()\n",
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"bottom.specgram(data_slice, Fs=sampling_rate)\n",
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"top.set_ylabel('U [V]')\n",
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"bottom.set_ylabel('F [Hz]')\n",
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"bottom.set_xlabel('t [s]')\n",
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"\n",
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"top.set_title('Voltage waveform')\n",
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"bottom.set_title('Voltage frequency spectrum')\n",
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"None"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"cell_type": "markdown",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Step 2: Calculate Short-Time Fourier Transform of capture"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Window length: 405 sp, zero-padded to 405 sp\n"
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]
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}
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],
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"source": [
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"fs = sampling_rate # Hz\n",
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"ff = 50 # Hz\n",
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"\n",
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"analysis_periods = 10\n",
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"analysis_periods = 20\n",
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"window_len = fs * analysis_periods/ff\n",
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"nfft_factor = 4\n",
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"nfft_factor = 1\n",
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"sigma = window_len/8 # samples\n",
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"\n",
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"f, t, Zxx = signal.stft(data,\n",
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" fs = fs,\n",
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" window=('gaussian', sigma),\n",
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" nperseg = window_len,\n",
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" nfft = window_len * nfft_factor)"
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" nfft = window_len * nfft_factor)\n",
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"print(f'Window length: {window_len:.0f} sp, zero-padded to {window_len * nfft_factor:.0f} sp')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Show a preview of STFT results\n",
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"\n",
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"Cut out our approximate frequency range of interest"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 64,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(200.0, 800.0)"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"window_len, window_len * nfft_factor"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"<ipython-input-64-467ca72791b1>: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",
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" fig, ax = plt.subplots(figsize=(9, 3))\n"
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]
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "cc101709475d440ea77e68bcb56ce3b7",
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"model_id": "95c94ad504b248febb55f81b0e919464",
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"version_major": 2,
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"version_minor": 0
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},
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@ -291,20 +352,34 @@
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"None"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Step 3: Run Gasior and Gonzalez for precise frequency estimation\n",
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"\n",
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"Limit analysis to frequency range of interest. If automatic adaption to totally different frequency ranges\n",
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"(e.g. 400Hz) would be necessary, we could switch here based on configuration or a lookup of the STFT bin\n",
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"containing highest overall energy.\n",
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"\n",
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"As elaborated in the Gasior and Gonzalez Paper [1] the shape of the template function should match the expected peak shape.\n",
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"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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 45,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "b0202d59643548cf83b6fa6fd7580d2d",
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"model_id": "5443a7d157cc4a828cbffc91b2d645e3",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"HBox(children=(FloatProgress(value=0.0, max=292611.0), HTML(value='')))"
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"HBox(children=(FloatProgress(value=0.0, max=2708.0), HTML(value='')))"
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]
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},
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"metadata": {},
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"f_t = t\n",
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"\n",
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"n_f, n_t = Zxx.shape\n",
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"# start, stop = 180, 220\n",
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"# start, stop = 90, 110\n",
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"# start, stop = 15, 35\n",
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"# bounds_f = slice(start // 4 * nfft_factor, stop // 4 * nfft_factor)\n",
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"# Frequency ROI\n",
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"f_min, f_max = 30, 70 # Hz\n",
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"# Indices of bins within ROI\n",
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"bounds_f = slice(np.argmax(f > f_min), np.argmin(f < f_max))\n",
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"\n",
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"\n",
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"# Initialize output array\n",
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"f_mean = np.zeros(Zxx.shape[1])\n",
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"\n",
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"# Iterate over STFT time slices\n",
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"for le_t in tnrange(1, Zxx.shape[1] - 1):\n",
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" # Cut out ROI and compute magnitude of complex fourier coefficients\n",
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" frame_f = f[bounds_f]\n",
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" frame_step = frame_f[1] - frame_f[0]\n",
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" time_step = f_t[1] - f_t[0]\n",
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" #if t == 10:\n",
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" # axs[-1].plot(frame_f, frame_Z)\n",
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" frame_Z = np.abs(Zxx[bounds_f, le_t])\n",
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" # frame_f = f[180:220]\n",
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" # frame_Z = np.abs(Zxx[180:220, 40])\n",
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" # frame_f = f[15:35]\n",
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" # frame_Z = np.abs(Zxx[15:35, 40])\n",
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" # plt.plot(frame_f, frame_Z)\n",
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"\n",
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" # peak_f = frame_f[np.argmax(frame)]\n",
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" # plt.axvline(peak_f, color='red')\n",
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"\n",
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"# def gauss(x, *p):\n",
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"# A, mu, sigma, o = p\n",
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"# return A*np.exp(-(x-mu)**2/(2.*sigma**2)) + o\n",
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"\n",
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" # Template function. We use a gaussian here. This function needs to fit the window above.\n",
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" def gauss(x, *p):\n",
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" A, mu, sigma = p\n",
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" return A*np.exp(-(x-mu)**2/(2.*sigma**2))\n",
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"\n",
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" f_start = frame_f[np.argmax(frame_Z)]\n",
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" A_start = np.max(frame_Z)\n",
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" # Calculate initial values for curve fitting\n",
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" f_start = frame_f[np.argmax(frame_Z)] # index of strongest bin index\n",
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" A_start = np.max(frame_Z) # strongest bin value\n",
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" p0 = [A_start, f_start, 1.]\n",
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" try:\n",
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" # Fit template to measurement data STFT ROI \n",
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" coeff, var = optimize.curve_fit(gauss, frame_f, frame_Z, p0=p0)\n",
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" # plt.plot(frame_f, gauss(frame_f, *coeff))\n",
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" #print(coeff)\n",
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" A, mu, sigma, *_ = coeff\n",
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" f_mean[le_t] = mu\n",
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" _A, f_mean[le_t], _sigma, *_ = coeff # The measured frequency is the mean of the fitted gaussian\n",
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" \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": 13,
|
||||
"execution_count": 56,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-56-4e12d8913585>: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), sharex=True)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "59d50a2876634433bdfb751a7a66d9ca",
|
||||
"model_id": "c1c391d0577f4dbeb59db8d1fa9261de",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
|
|
@ -392,49 +471,45 @@
|
|||
"fig, ax = plt.subplots(figsize=(9, 5), sharex=True)\n",
|
||||
"fig.tight_layout(pad=2.2, h_pad=0, w_pad=1)\n",
|
||||
"\n",
|
||||
"label = f'Run {last_run}'\n",
|
||||
"ax.plot(f_t[1:-1], f_mean[1:-1])\n",
|
||||
"\n",
|
||||
"# b, a = signal.butter(3,\n",
|
||||
"# 1/5, # Hz\n",
|
||||
"# btype='lowpass',\n",
|
||||
"# fs=1/time_step)\n",
|
||||
"# filtered = signal.lfilter(b, a, f_mean[1:-1], axis=0)\n",
|
||||
"# ax.plot(f_t[1:-1], filtered)\n",
|
||||
"\n",
|
||||
"ax.set_title(label, pad=-20)\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",
|
||||
"if not label in ['off_frequency', 'sweep_phase_steps']:\n",
|
||||
" ax.set_ylim([49.90, 50.10])\n",
|
||||
" var = np.var(f_mean[~np.isnan(f_mean)][1:-1])\n",
|
||||
" ax.text(0.5, 0.08, f'σ²={var * 1e3:.3g} mHz²', transform=ax.transAxes, ha='center', color='white', bbox=bbox)\n",
|
||||
" ax.text(0.5, 0.15, f'σ={np.sqrt(var) * 1e3:.3g} mHz', transform=ax.transAxes, ha='center', color='white', bbox=bbox)\n",
|
||||
"\n",
|
||||
"# ax.text(0.5, 0.2, f'filt. σ²={np.var(filtered) * 1e3:.3g} mHz', transform=ax.transAxes, ha='center')\n",
|
||||
"else:\n",
|
||||
" f_min, f_max = min(f_mean[1:-1]), max(f_mean[1:-1])\n",
|
||||
" delta = f_max - f_min\n",
|
||||
" ax.set_ylim(f_min - delta * 0.1, f_max + delta * 0.3)\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 [s]')\n",
|
||||
"ax.set_xlabel('recording time t [hh:mm:ss]')\n",
|
||||
"None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"execution_count": 57,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-57-8b77e38496af>:9: 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, (ax2, ax1) = plt.subplots(2, figsize=(9,7))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "95cfea97c3b946ed9cdf351b16c2c45e",
|
||||
"model_id": "c1209b4895814c92a9b0fa01ad666667",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
|
|
@ -444,6 +519,17 @@
|
|||
},
|
||||
"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-57-8b77e38496af>\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": [
|
||||
|
|
@ -512,7 +598,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"execution_count": 69,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -531,49 +617,16 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 53,
|
||||
"execution_count": 73,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-53-c54c3e4ac2be>:20: 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=(5, 2))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "ad5454f664734681adb8640f480ce69a",
|
||||
"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": [
|
||||
"Text(20, 1, '50 Hz')"
|
||||
]
|
||||
},
|
||||
"execution_count": 53,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Number of samplepoints\n",
|
||||
"N = len(data)\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 * sig.blackman(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",
|
||||
|
|
@ -590,21 +643,21 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 68,
|
||||
"execution_count": 77,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-68-21b49a5af249>: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",
|
||||
"<ipython-input-77-2f4bcf6b2d33>: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=(6, 3))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "4a3edb0925fe47eb8751150aa7da8c22",
|
||||
"model_id": "8b689c4f96fa40ffb5012764afb57564",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
|
|
@ -631,7 +684,7 @@
|
|||
"ax.set_xlabel('f [Hz]')\n",
|
||||
"ax.set_ylabel('Amplitude V [V]')\n",
|
||||
"ax.grid()\n",
|
||||
"ax.set_xlim([0.1, 500])\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",
|
||||
|
|
@ -646,21 +699,21 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"execution_count": 84,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-43-2e31f0cb9460>:21: 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",
|
||||
"<ipython-input-84-936ca777d145>:26: 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": "37e159955f114f36824dd42da060b9ea",
|
||||
"model_id": "b58b8858dea1485fae236c9fbb6954d5",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
|
|
@ -670,21 +723,15 @@
|
|||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"[<matplotlib.lines.Line2D at 0x7fafc108cdc0>]"
|
||||
]
|
||||
},
|
||||
"execution_count": 43,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"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",
|
||||
|
|
@ -715,8 +762,8 @@
|
|||
"#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:])"
|
||||
"#ax.set_ylim([5e-7, 2e-2])\n",
|
||||
"#ax.plot(xf[1:], 2e-6/xf[1:])"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -744,6 +791,15 @@
|
|||
"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": {
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue