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2025-10-21 11:20:44 +08:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"# Plotting and manipulating FFTs for filtering\n",
"\n",
"Plot the power of the FFT of a signal and inverse FFT back to reconstruct\n",
"a signal.\n",
"\n",
"This example demonstrate :func:`scipy.fft.fft`,\n",
":func:`scipy.fft.fftfreq` and :func:`scipy.fft.ifft`. It\n",
"implements a basic filter that is very suboptimal, and should not be\n",
"used.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate the signal\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10bbc9dc0>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Seed the random number generator\n",
"rng = np.random.default_rng(27446968)\n",
"\n",
"time_step = 0.02\n",
"period = 5.0\n",
"\n",
"time_vec = np.arange(0, 20, time_step)\n",
"sig = np.sin(2 * np.pi / period * time_vec) + 0.5 * rng.normal(size=time_vec.size)\n",
"\n",
"plt.figure(figsize=(6, 5))\n",
"plt.plot(time_vec, sig, label=\"Original signal\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Compute and plot the power\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# The FFT of the signal\n",
"sig_fft = sp.fft.fft(sig)\n",
"\n",
"# And the power (sig_fft is of complex dtype)\n",
"power = np.abs(sig_fft) ** 2\n",
"\n",
"# The corresponding frequencies\n",
"sample_freq = sp.fft.fftfreq(sig.size, d=time_step)\n",
"\n",
"# Plot the FFT power\n",
"plt.figure(figsize=(6, 5))\n",
"plt.plot(sample_freq, power)\n",
"plt.xlabel(\"Frequency [Hz]\")\n",
"plt.ylabel(\"plower\")\n",
"\n",
"# Find the peak frequency: we can focus on only the positive frequencies\n",
"pos_mask = np.where(sample_freq > 0)\n",
"freqs = sample_freq[pos_mask]\n",
"peak_freq = freqs[power[pos_mask].argmax()]\n",
"\n",
"# Check that it does indeed correspond to the frequency that we generate\n",
"# the signal with\n",
"np.allclose(peak_freq, 1.0 / period)\n",
"\n",
"# An inner plot to show the peak frequency\n",
"axes = plt.axes((0.55, 0.3, 0.3, 0.5))\n",
"plt.title(\"Peak frequency\")\n",
"plt.plot(freqs[:8], power[pos_mask][:8])\n",
"plt.setp(axes, yticks=[])\n",
"\n",
"# scipy.signal.find_peaks_cwt can also be used for more advanced\n",
"# peak detection"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Remove all the high frequencies\n",
"\n",
" We now remove all the high frequencies and transform back from\n",
" frequencies to signal.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/miniconda3/envs/pyscixx/lib/python3.12/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" return math.isfinite(val)\n",
"/opt/miniconda3/envs/pyscixx/lib/python3.12/site-packages/matplotlib/cbook.py:1355: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" return np.asarray(x, float)\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11cf1ae70>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 600x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"high_freq_fft = sig_fft.copy()\n",
"high_freq_fft[np.abs(sample_freq) > peak_freq] = 0\n",
"filtered_sig = sp.fft.ifft(high_freq_fft)\n",
"\n",
"plt.figure(figsize=(6, 5))\n",
"plt.plot(time_vec, sig, label=\"Original signal\")\n",
"plt.plot(time_vec, filtered_sig, linewidth=3, label=\"Filtered signal\")\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.ylabel(\"Amplitude\")\n",
"\n",
"plt.legend(loc=\"best\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Note** This is actually a bad way of creating a filter: such brutal\n",
"cut-off in frequency space does not control distortion on the signal.\n",
"\n",
"Filters should be created using the SciPy filter design code\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"plt.show()"
]
},
{
"cell_type": "code",
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