{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Low Pass"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
],
"text/vnd.plotly.v1+html": [
"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# https://plot.ly/python/subplots/\n",
"import plotly as py\n",
"import plotly.graph_objs as go\n",
"# from plotly.offline import download_plotlyjs\n",
"\n",
"py.offline.init_notebook_mode(connected=True)\n",
"\n",
"import numpy as np\n",
"from sklearn.metrics import mean_squared_error\n",
"\n",
"def print_mse(got, predicted, prefix=''):\n",
" mse = mean_squared_error(got, predicted)\n",
" if isinstance(mse, np.complex):\n",
" print('%s Mean Squared Error: (%.2g, %.2g)' % (prefix, mse.real, mse.imag))\n",
" else:\n",
" print('%s Mean Squared Error: %.2g' % (prefix, mse))\n",
" \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# фильтр скользящего среднего\n",
"def create_filter_median(kernel_size):\n",
" if kernel_size % 2 == 0:\n",
" raise ValueError(\"kernel_size should be odd\")\n",
" return [1 / kernel_size for i in range(kernel_size)]\n",
" \n",
"def apply_filter_median(signal, filt):\n",
" return np.convolve(signal, filt, mode='valid')\n",
"\n",
"def impulse_response_median(filt):\n",
" f = np.pad(filt, (0, len(filt) * 4), 'constant', constant_values=(0,0))\n",
" return np.fft.fft(f)[:int(len(f) / 2)]\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"[ (2,1) x2,y2 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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]
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"metadata": {},
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}
],
"source": [
"N = 500\n",
"kernel_size = 71\n",
"T = 1.0 # s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s = np.random.rand(N)\n",
"\n",
"filt = create_filter_median(kernel_size)\n",
"fs = apply_filter_median(s, filt)\n",
"ir = impulse_response_median(filt)\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = fs,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_ir = go.Scatter(\n",
" x = [i for i in range(len(ir.real))],\n",
" y = np.absolute(ir),\n",
" name='impulse response'\n",
")\n",
"\n",
"\n",
"fig = py.tools.make_subplots(rows = 2, cols = 1)\n",
"\n",
"fig['layout'].update(height=900, width=900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"\n",
"fig.append_trace(tr_ir, 2, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def prod(iterable):\n",
" from functools import reduce\n",
" from operator import mul\n",
" return reduce(mul, iterable, 1)\n",
"\n",
"def transfer_function_butterworth(Rp, Rs, w0, w1):\n",
" ep = np.sqrt(np.power(10, Rp / 10.) - 1)\n",
" es = np.sqrt(np.power(10, Rs / 10.) - 1)\n",
" k = w0 / w1\n",
" k1 = ep / es\n",
" N = int(np.ceil(np.log(k1) / np.log(k)))\n",
" L = N // 2\n",
" r = N % 2\n",
" a = np.power(ep, - 1. / N)\n",
" th = [(2 * n + 1) / 2 / N * np.pi for n in range(L)]\n",
" \n",
" return lambda s: 1. / (ep * np.power(s + a, r) * prod(s*s + 2*a*np.sin(thn)*s + a*a for thn in th))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 200\n",
"T = 2# s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s = np.ones(N)\n",
"\n",
"df = 1. / T\n",
"k = [i * df for i in range(N)]\n",
"\n",
"Rp = 1.0\n",
"Rs = 30.0\n",
"w0 = 1\n",
"w1 = 5\n",
"HGen = transfer_function_butterworth(Rp, Rs, w0, w1)\n",
"\n",
"H_jw = [HGen(1j*i / w0) for i in k]\n",
"afr = np.absolute(H_jw)\n",
"phase = np.angle(H_jw)\n",
"\n",
"# sym = np.append(afr[::-1], afr)\n",
"coef = np.fft.ifft(afr)\n",
"# coef = [HGen((1 - 1. / z) / (1 + 1. / z) * 2 * N/T) for z in t[1:]]\n",
"# coef = coef[:len(coef) // 2]\n",
"\n",
"\n",
"coef[50:-50] = 0\n",
"H_jw = np.fft.fft(coef.real)\n",
"afr = np.absolute(H_jw)\n",
"afr = afr[:len(afr) // 2]\n",
"\n",
"\n",
"#--- \n",
"kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"filt = np.pad(filt, (0, N - kernel_size), 'constant', constant_values=(0, 0))\n",
"# ir_median = impulse_response_median(filt)\n",
"ir_median = np.fft.fft(filt)[:len(filt) // 2]\n",
"#---\n",
"\n",
"\n",
"tr_afr = go.Scatter(\n",
" x = k,\n",
" y = afr,\n",
" name='Amplitude Frequency Response'\n",
")\n",
"\n",
"tr_ir_median = go.Scatter(\n",
" x = k,\n",
" y = np.absolute(ir_median),\n",
" name='ir median'\n",
")\n",
"tr_coef_real = go.Scatter(\n",
" x = t,\n",
" y = coef.real,\n",
" name='coef real'\n",
")\n",
"\n",
"tr_coef_imag = go.Scatter(\n",
" x = t,\n",
" y = coef.imag,\n",
" name='coef imag'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"# fig['layout'].update(xaxis=dict(type='log', autorange=True),\n",
"# xaxis2=dict(type='log', autorange=True),\n",
"# xaxis3=dict(type='log', autorange=True))\n",
"\n",
"fig.append_trace(tr_afr, 1, 1)\n",
"fig.append_trace(tr_ir_median, 1, 1)\n",
"# fig.append_trace(tr_phase, 2, 1)\n",
"# fig.append_trace(tr_coef_real, 2, 1)\n",
"# fig.append_trace(tr_coef_imag, 2, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
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1.0], \"anchor\": \"x1\"}, \"height\": 450, \"width\": 900}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1 = 1\n",
"f2 = 8\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"s = [np.sin(w1 * i) + np.sin(w2 * i) for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1 = 1\n",
"f2 = 8\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"s = [np.sin(w1 * i) + np.sin(w2 * i) for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"#filt = np.pad(filt, (0, N - kernel_size), 'constant', constant_values=(0, 0))\n",
"filtered_median = np.append(np.zeros(kernel_size // 2), np.convolve(s, filt, mode = 'valid'))\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_median = go.Scatter(\n",
" x = t,\n",
" y = filtered_median,\n",
" name='filtered median'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"fig.append_trace(tr_median, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f = 1\n",
"w = 2 * np.pi * f\n",
"\n",
"count = 4\n",
"s = [sum(np.cos(w * i * 2*k) for k in range(count)) for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"#filt = np.pad(filt, (0, N - kernel_size), 'constant', constant_values=(0, 0))\n",
"filtered_median = np.append(np.zeros(kernel_size // 2), np.convolve(s, filt, mode = 'valid'))\n",
"\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_median = go.Scatter(\n",
" x = t,\n",
" y = filtered_median,\n",
" name='filtered median'\n",
")\n",
"\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"fig.append_trace(tr_median, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
"data": [
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\"name\": \"filtered sliding\", \"xaxis\": \"x1\", \"yaxis\": \"y1\"}], {\"xaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"y1\"}, \"yaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"x1\"}, \"height\": 450, \"width\": 900}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
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"source": [
"f = 1\n",
"w = 2 * np.pi * f1\n",
"\n",
"s = [np.sin(w * i) + np.random.rand() for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"#kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"\n",
"filtered_median = np.pad(np.convolve(s, filt, mode = 'valid'), (kernel_size // 2, kernel_size // 2), 'constant', constant_values = (0, 0))\n",
"\n",
"#-----\n",
"# filtered = s - filtered\n",
"# filtered_median = s - filtered_median\n",
"#-----\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_median = go.Scatter(\n",
" x = t,\n",
" y = filtered_median,\n",
" name='filtered sliding'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"fig.append_trace(tr_median, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# High Pass (1 - Low Pass)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
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"source": [
"N = 200\n",
"T = 2# s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s = np.ones(N)\n",
"\n",
"df = 1. / T\n",
"k = [i * df for i in range(N)]\n",
"\n",
"Rp = 1.0\n",
"Rs = 30.0\n",
"w0 = 10\n",
"w1 = 15\n",
"HGen = transfer_function_butterworth(Rp, Rs, w0, w1)\n",
"\n",
"H_jw = [HGen(1j*i / w0) for i in k]\n",
"afr = np.absolute(H_jw)\n",
"phase = np.angle(H_jw)\n",
"coef = np.fft.ifft(afr)\n",
"\n",
"\n",
"coef[50:-50] = 0\n",
"H_jw = np.fft.fft(coef.real)\n",
"afr = np.absolute(H_jw)\n",
"afr = afr[:len(afr) // 2]\n",
"\n",
"\n",
"#--- \n",
"kernel_size = 7\n",
"filt = create_filter_median(kernel_size)\n",
"filt = np.pad(filt, (0, N - kernel_size), 'constant', constant_values=(0, 0))\n",
"ir_median = np.fft.fft(filt)[:len(filt) // 2]\n",
"\n",
"\n",
"afr = [1 - i for i in afr]\n",
"ir_median = [1 - i for i in ir_median]\n",
"#---\n",
"\n",
"\n",
"tr_afr = go.Scatter(\n",
" x = k,\n",
" y = afr,\n",
" name='Amplitude Frequency Response'\n",
")\n",
"\n",
"tr_ir_median = go.Scatter(\n",
" x = k,\n",
" y = np.absolute(ir_median),\n",
" name='ir median'\n",
")\n",
"tr_coef_real = go.Scatter(\n",
" x = t,\n",
" y = coef.real,\n",
" name='coef real'\n",
")\n",
"\n",
"tr_coef_imag = go.Scatter(\n",
" x = t,\n",
" y = coef.imag,\n",
" name='coef imag'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_afr, 1, 1)\n",
"fig.append_trace(tr_ir_median, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1 = 1\n",
"f2 = 8\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"s = [np.sin(w1 * i) + np.sin(w2 * i) for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"#kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"\n",
"filtered_median = np.pad(np.convolve(s, filt, mode = 'valid'), (kernel_size // 2, kernel_size // 2), 'constant', constant_values = (0, 0))\n",
"\n",
"#-----\n",
"filtered = s - filtered\n",
"filtered_median = s - filtered_median\n",
"#-----\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_median = go.Scatter(\n",
" x = t,\n",
" y = filtered_median,\n",
" name='filtered sliding'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"fig.append_trace(tr_median, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f = 1\n",
"w = 2 * np.pi * f\n",
"\n",
"count = 4\n",
"s = [sum(np.cos(w * i * 2*k) for k in range(count)) for i in t]\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"#kernel_size = 31\n",
"filt = create_filter_median(kernel_size)\n",
"\n",
"filtered_median = np.pad(np.convolve(s, filt, mode = 'valid'), (kernel_size // 2, kernel_size // 2), 'constant', constant_values = (0, 0))\n",
"\n",
"#-----\n",
"filtered = s - filtered\n",
"filtered_median = s - filtered_median\n",
"#-----\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"tr_median = go.Scatter(\n",
" x = t,\n",
" y = filtered_median,\n",
" name='filtered sliding'\n",
")\n",
"\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"fig.append_trace(tr_median, 1, 1)\n",
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-0.021377335980674896, -0.16253172670495297], \"name\": \"coef real\", \"xaxis\": \"x1\", \"yaxis\": \"y1\"}], {\"xaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"y1\"}, \"yaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"x1\"}, \"height\": 450, \"width\": 900}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
]
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 100\n",
"T = 1# s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s = np.ones(N)\n",
"\n",
"df = 1. / T\n",
"k = [i * df for i in range(N)]\n",
"\n",
"Rp = 1.0\n",
"Rs = 30.0\n",
"w0 = 20\n",
"w1 = 25\n",
"HGen = transfer_function_butterworth_high_pass(Rp, Rs, w0, w1)\n",
"\n",
"H_jw = [0 if i == 0 else HGen(1j*i / w1) for i in k]\n",
"afr = np.absolute(H_jw)\n",
"phase = np.angle(H_jw)\n",
"coef = np.fft.ifft(afr)\n",
"\n",
"\n",
"# coef[20:] = 0\n",
"# H_jw = np.fft.fft(coef.real)\n",
"# afr = np.absolute(H_jw)\n",
"afr = afr[:len(afr) // 2]\n",
"# afr[0] = 0\n",
"\n",
"tr_afr = go.Scatter(\n",
" x = k,\n",
" y = afr,\n",
" name='Amplitude Frequency Response'\n",
")\n",
"\n",
"tr_coef_real = go.Scatter(\n",
" x = k,\n",
" y = coef.real,\n",
" name='coef real'\n",
")\n",
"\n",
"tr_coef_imag = go.Scatter(\n",
" x = t,\n",
" y = coef.imag,\n",
" name='coef imag'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_afr, 1, 1)\n",
"fig.append_trace(tr_coef_real, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 161,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
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"source": [
"f = 5\n",
"w = 2 * np.pi * f\n",
"\n",
"# t = np.linspace(0, T, N)\n",
"\n",
"s = [np.sin(w * i) + np.random.rand() for i in t]\n",
"fft = np.fft.fft(s)\n",
"\n",
"filtsym = np.append(afr[::-1], afr)\n",
"\n",
"filtered = np.fft.ifft(np.fft.fft(s) * filtsym).real\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {},
"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1 = 1\n",
"f2 = 25\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"s = [np.sin(w1 * i) + np.sin(w2 * i) for i in t]\n",
"fft = np.fft.fft(s)\n",
"\n",
"filtsym = np.append(afr, afr[::-1])\n",
"\n",
"filtered = np.fft.ifft(fft * filtsym).real\n",
"\n",
"tr_s = go.Scatter(\n",
" x = t,\n",
" y = s,\n",
" name='signal'\n",
")\n",
"\n",
"tr_fs = go.Scatter(\n",
" x = t,\n",
" y = filtered,\n",
" name='filtered'\n",
")\n",
"\n",
"rows = 1\n",
"cols = 1\n",
"fig = py.tools.make_subplots(rows = rows, cols = cols)\n",
"\n",
"fig['layout'].update(height=rows * 450, width=cols * 900)\n",
"\n",
"fig.append_trace(tr_s, 1, 1)\n",
"fig.append_trace(tr_fs, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}