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@CoolOppo
Created October 19, 2019 07:11
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How to extract frequencies with numpy using the real discrete fourier transform
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{
"cells": [
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import math"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [],
"source": [
"# gets magnitude of complex number\n",
"def imagnitude(cplx):\n",
" return math.sqrt(cplx.real ** 2 + cplx.imag ** 2)\n",
"\n",
"# same function which works element-wise\n",
"vimag = np.vectorize(imagnitude)"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1d4b4f569c8>]"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"d=.01 # timestep\n",
"\n",
"x=np.arange(0,10,d)\n",
"\n",
"\n",
"# if frequency = 2*pi*x, frequency = 1 second\n",
"\n",
"# make two sine waves with frequencies 1 Hz and 5 Hz,\n",
"# with the 5 Hz one being twice as strong:\n",
"y = np.sin(x*np.pi*2.0) + 2*np.sin(x*np.pi*10.0)\n",
"\n",
"plt.plot(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1d4b4fc1408>]"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# compute the real fft and get the magnitude of the elements:\n",
"y_fft=vimag(np.fft.rfft(y)) \n",
"\n",
"# get the frequencies each element of y_fft actually represents:\n",
"# (since we put in d here, it will have the same length as our array,\n",
"# which was also generated using d-sized steps)\n",
"x2=np.fft.rfftfreq(len(x),d)\n",
"\n",
"# bring within 0-1 range\n",
"y2=y_fft/y_fft.max()\n",
"\n",
"plt.plot(x2, y2)"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1d4b5024688>]"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x,np.fft.irfft(vimag(y_fft)))"
]
}
],
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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