Repo re-org

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+{
+ "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
+}