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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "4b15d9c3",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4e9129a5",
"metadata": {},
"outputs": [],
"source": [
"# Do not try to mask unused channels to optimize the code: we have tried it and it was in fact COUNTER-PRODUCTIVE.\n",
"# Python is the bottleneck with 8 channels, not numpy, and it does not matter whether we use all 8 or 0 channels.\n",
"\n",
"def shift_numpy(arr, num, fill_value=np.nan):\n",
" result = np.empty_like(arr)\n",
" if num > 0:\n",
" result[:num] = fill_value\n",
" result[num:] = arr[:-num]\n",
" elif num < 0:\n",
" result[num:] = fill_value\n",
" result[:num] = arr[-num:]\n",
" else:\n",
" result[:] = arr\n",
" return result\n",
"\n",
"\n",
"class FIR:\n",
" def __init__(self, nb_channels, coefficients, buffer=None):\n",
" \n",
" self.coefficients = np.expand_dims(np.array(coefficients), axis=1)\n",
" self.taps = len(self.coefficients)\n",
" self.nb_channels = nb_channels\n",
" self.buffer = np.array(z) if buffer is not None else np.zeros((self.taps, self.nb_channels))\n",
" \n",
" def filter(self, x):\n",
" self.buffer = shift_numpy(self.buffer, 1, x)\n",
" filtered = np.sum(self.buffer * self.coefficients, axis=0)\n",
" return filtered\n",
"\n",
" \n",
"class FilterPipeline:\n",
" def __init__(self, nb_channels, power_line_fq=60):\n",
" self.nb_channels = nb_channels\n",
" assert power_line_fq in [50, 60], f\"The only supported power line frequencies are 50Hz and 60Hz\"\n",
" if power_line_fq == 60:\n",
" self.notch_coeff1 = -0.12478308884588535\n",
" self.notch_coeff2 = 0.98729186796473023\n",
" self.notch_coeff3 = 0.99364593398236511\n",
" self.notch_coeff4 = -0.12478308884588535\n",
" self.notch_coeff5 = 0.99364593398236511\n",
" else:\n",
" self.notch_coeff1 = -0.61410695998423581\n",
" self.notch_coeff2 = 0.98729186796473023\n",
" self.notch_coeff3 = 0.99364593398236511\n",
" self.notch_coeff4 = -0.61410695998423581\n",
" self.notch_coeff5 = 0.99364593398236511\n",
" self.dfs = [np.zeros(self.nb_channels), np.zeros(self.nb_channels)]\n",
" \n",
" self.moving_average = None\n",
" self.moving_variance = np.zeros(self.nb_channels)\n",
" self.ALPHA_AVG = 0.1\n",
" self.ALPHA_STD = 0.001\n",
" self.EPSILON = 0.000001\n",
" \n",
" self.fir_30_coef = [\n",
" 0.001623780150148094927192721215192250384,\n",
" 0.014988684599373741992978104065059596905,\n",
" 0.021287595318265635502275046064823982306,\n",
" 0.007349500393709578957568417933998716762,\n",
" -0.025127515717112181709014251396183681209,\n",
" -0.052210507359822452833064687638398027048,\n",
" -0.039273839505489904766477593511808663607,\n",
" 0.033021568427940004020193498490698402748,\n",
" 0.147606943281569008563636202779889572412,\n",
" 0.254000252034505602516389899392379447818,\n",
" 0.297330876398883392486283128164359368384,\n",
" 0.254000252034505602516389899392379447818,\n",
" 0.147606943281569008563636202779889572412,\n",
" 0.033021568427940004020193498490698402748,\n",
" -0.039273839505489904766477593511808663607,\n",
" -0.052210507359822452833064687638398027048,\n",
" -0.025127515717112181709014251396183681209,\n",
" 0.007349500393709578957568417933998716762,\n",
" 0.021287595318265635502275046064823982306,\n",
" 0.014988684599373741992978104065059596905,\n",
" 0.001623780150148094927192721215192250384]\n",
" self.fir = FIR(self.nb_channels, self.fir_30_coef)\n",
" \n",
" def filter(self, value):\n",
" \"\"\"\n",
" value: a numpy array of shape (data series, channels)\n",
" \"\"\"\n",
" for i, x in enumerate(value): # loop over the data series\n",
" # FIR:\n",
" x = self.fir.filter(x)\n",
" # notch:\n",
" denAccum = (x - self.notch_coeff1 * self.dfs[0]) - self.notch_coeff2 * self.dfs[1]\n",
" x = (self.notch_coeff3 * denAccum + self.notch_coeff4 * self.dfs[0]) + self.notch_coeff5 * self.dfs[1]\n",
" self.dfs[1] = self.dfs[0]\n",
" self.dfs[0] = denAccum\n",
" # standardization:\n",
" if self.moving_average is not None:\n",
" delta = x - self.moving_average\n",
" self.moving_average = self.moving_average + self.ALPHA_AVG * delta\n",
" self.moving_variance = (1 - self.ALPHA_STD) * (self.moving_variance + self.ALPHA_STD * delta**2)\n",
" moving_std = np.sqrt(self.moving_variance)\n",
" x = (x - self.moving_average) / (moving_std + self.EPSILON)\n",
" else:\n",
" self.moving_average = x\n",
" value[i] = x\n",
" return value"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "80fc186e",
"metadata": {},
"outputs": [],
"source": [
"duration = 1\n",
"fsample = 250\n",
"f1 = 15\n",
"f2 = 50\n",
"f3 = 60\n",
"f4 = 100\n",
"f5 = 70\n",
"f6 = 80\n",
"f7 = 90\n",
"scale = 4.0e-5\n",
"\n",
"w1 = 2*np.pi*f1\n",
"w2 = 2*np.pi*f2\n",
"w3 = 2*np.pi*f3\n",
"w4 = 2*np.pi*f4\n",
"w5 = 2*np.pi*f5\n",
"w6 = 2*np.pi*f6\n",
"w7 = 2*np.pi*f7\n",
"nb_samples = int(duration*fsample)\n",
"\n",
"sig1 = np.array([np.sin(w1*i/fsample) for i in range(nb_samples)])\n",
"sig2 = np.array([np.sin(w2*i/fsample) for i in range(nb_samples)])\n",
"sig3 = np.array([np.sin(w3*i/fsample) for i in range(nb_samples)])\n",
"sig4 = np.array([np.sin(w4*i/fsample) for i in range(nb_samples)])\n",
"sig5 = np.array([np.sin(w5*i/fsample) for i in range(nb_samples)])\n",
"sig6 = np.array([np.sin(w6*i/fsample) for i in range(nb_samples)])\n",
"sig7 = np.array([np.sin(w7*i/fsample) for i in range(nb_samples)])\n",
"sig8 = sig1 + sig2 + sig3 + sig4 + sig5 + sig6 + sig7\n",
"\n",
"v = np.array([sig1, sig2, sig3, sig4, sig5, sig6, sig7, sig8]).T * scale\n",
"\n",
"mask = [0,0,0,0,0,0,0,1]\n",
"\n",
"v.shape"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b974a851",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"plt.figure(figsize=(20,5))\n",
"plt.plot(v[:, 7])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d2b7145c",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"print(mask)\n",
"fp = FilterPipeline(nb_channels=8, power_line_fq=60)\n",
"\n",
"ts = time.time()\n",
"v = fp.filter(v)\n",
"print(time.time() - ts)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "70235c0a",
"metadata": {},
"outputs": [],
"source": [
"plt.figure(figsize=(20,10))\n",
"plt.plot(v[:, 7])"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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