{ "cells": [ { "cell_type": "code", "execution_count": 24, "id": "ada8e74b", "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad\n", "from scipy.fft import fft, fftfreq\n", "from math import pi, sin, cos\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy as smp" ] }, { "cell_type": "markdown", "id": "f84529bd", "metadata": {}, "source": [ "This is based upon the video series https://www.youtube.com/playlist?list=PLB24BC7956EE040CD\n", "\n", "The formula to calculate the fourier coefficients is basically the following:\n", "$$ C_k = \\int_0^1 e^{(-2 \\pi i k t)} f(t) dt $$" ] }, { "cell_type": "code", "execution_count": 2, "id": "4d386691", "metadata": {}, "outputs": [], "source": [ "class Fourier:\n", " def __init__(self, fn):\n", " self.fn = fn\n", "\n", " def ck(self,k):\n", " def f_real(t):\n", " res = self.fn(t)*cos(-2*pi*k*t)\n", " return res\n", " def f_imag(t):\n", " res = self.fn(t)*sin(-2*pi*k*t)\n", " return res\n", " \n", " realpart = quad(f_real, 0, 1, limit=100)[0]\n", "\n", " imagpart = quad(f_imag, 0, 1, limit=100)[0]\n", " return complex(realpart, imagpart)\n", " def ck2(self, k):\n", " if k == 0:\n", " return self.ck(0).real\n", " else:\n", " result = self.ck(k) + self.ck(-k).conjugate()\n", " #print ('**',k, self.ck(k), self.ck(-k))\n", " return result\n", " \n", " def freq(self, N):\n", " xvals = []\n", " yvals = []\n", " for k in range(0, N+1):\n", " result = self.ck2(k)\n", " xvals.append(k)\n", " yvals.append(result)\n", "\n", " return (xvals, yvals)\n", " \n", " def plot_frequencies(self, harmonics=40):\n", " xvals, yvals = self.freq(harmonics)\n", " yr = list(map(lambda x: x.real, yvals))\n", " yi = list(map(lambda x: x.imag, yvals))\n", " fig, ax = plt.subplots()\n", " ax.bar(xvals, yr, color='orange', label='even')\n", " xvals2 = list(map(lambda x: x+.5, xvals))\n", " ax.bar(xvals2, yi, color='blue', label='odd')\n", " ax.legend()\n", " ax.grid()\n", " plt.show()\n", " \n", " def plot_reconstructions(self, max_harmonics):\n", " cols = 3\n", " rows = 2\n", "\n", " fig, axs = plt.subplots(rows, cols, squeeze=True)\n", " fig.set_size_inches(12,8)\n", " #print (axs)\n", " #harmonics = [4,6,10,16,30, 60]\n", " for idx1 in range(0, rows):\n", " for idx2 in range(0, cols):\n", "\n", " axs[idx1][idx2].grid()\n", " trange = np.linspace(0,4, num=400)\n", " yrange = np.zeros_like(trange)\n", "\n", " h = max_harmonics.pop()\n", " xvals, yvals = self.freq(h)\n", " yr = list(map(lambda x: x.real, yvals))\n", " yi = list(map(lambda x: x.imag, yvals))\n", " for ii, t in enumerate(trange):\n", "\n", " for k in range(0, h):\n", " yrange[ii] += yi[k]*sin(2*pi*k*t) + yr[k]*cos(2*pi*k*t)\n", " axs[rows - idx1 -1][cols - idx2 -1].set_title(\"N = {}\".format(h)) \n", " axs[rows - idx1 -1][cols - idx2 -1].plot(trange, yrange)\n", "\n", " def plot_single(self, harmonics=100):\n", " fig, ax = plt.subplots()\n", " trange = np.linspace(0,4, num=400)\n", " yrange = np.zeros_like(trange)\n", " xvals, yvals = self.freq(harmonics)\n", " yr = list(map(lambda x: x.real, yvals))\n", " yi = list(map(lambda x: x.imag, yvals))\n", " for ii, t in enumerate(trange):\n", " for k in range(0, harmonics):\n", " yrange[ii] += yi[k]*sin(2*pi*k*t) + yr[k]*cos(2*pi*k*t)\n", " ax.grid()\n", " plt.plot(trange, yrange)\n", " \n", "\n" ] }, { "cell_type": "markdown", "id": "7a7d08ab", "metadata": {}, "source": [ "We define a square wave" ] }, { "cell_type": "code", "execution_count": 27, "id": "bed5f2ff", "metadata": {}, "outputs": [], "source": [ "def fn(t):\n", " if t < 0.25 or t > .75:\n", " return 1\n", " else:\n", " return 0" ] }, { "cell_type": "code", "execution_count": 4, "id": "1d6a6784", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0,1)\n", "ff = np.vectorize(fn)\n", "y = ff(x)\n", "ax = plt.gca()\n", "ax.grid()\n", "plt.plot(x,y)" ] }, { "cell_type": "code", "execution_count": 5, "id": "2b4e7e6f", "metadata": {}, "outputs": [], "source": [ "fourier = Fourier(fn)" ] }, { "cell_type": "code", "execution_count": 6, "id": "22f4f45f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fourier.plot_frequencies()" ] }, { "cell_type": "code", "execution_count": 47, "id": "5d25c3b2", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 1000\n", "T = 1/1000\n", "x = np.linspace(0.0, N*T, N, endpoint=False)\n", "y = np.vectorize(fn)(x)\n", "yf = fft(y)\n", "xf = fftfreq(N, T)[:N//2]\n", "plt.xlim(right=100)\n", "plt.plot(xf, 2/N*np.abs(yf[0:N//2]))\n", "#plt.plot(xf, 2/N*(yf[0:N//2]).imag)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "a921f769", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fourier.plot_reconstructions(max_harmonics = [4,6,10,16,30, 60])" ] }, { "cell_type": "markdown", "id": "9bddb30a", "metadata": {}, "source": [ "To look at the same think analytically" ] }, { "cell_type": "code", "execution_count": 9, "id": "11f1eacf", "metadata": {}, "outputs": [], "source": [ "k, T = smp.symbols(\"k T\", integer=True)\n", "t = smp.symbols(\"t\", real=True)" ] }, { "cell_type": "code", "execution_count": 10, "id": "f934fd5c", "metadata": {}, "outputs": [], "source": [ "smp.init_printing(use_latex=True)" ] }, { "cell_type": "code", "execution_count": 11, "id": "e3f3beae", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle e^{- 2 i \\pi k t}$" ], "text/plain": [ " -2⋅ⅈ⋅π⋅k⋅t\n", "ℯ " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq = smp.exp(-2*smp.pi*smp.I * t * k)\n", "eq" ] }, { "cell_type": "code", "execution_count": 12, "id": "c7f9eb60", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\begin{cases} - \\frac{i}{2 \\pi k} + \\frac{i e^{- 0.5 i \\pi k}}{2 \\pi k} & \\text{for}\\: k \\neq 0 \\\\0.25 & \\text{otherwise} \\end{cases}$" ], "text/plain": [ "⎧ -0.5⋅ⅈ⋅π⋅k \n", "⎪ ⅈ ⅈ⋅ℯ \n", "⎪- ───── + ───────────── for k ≠ 0\n", "⎨ 2⋅π⋅k 2⋅π⋅k \n", "⎪ \n", "⎪ 0.25 otherwise\n", "⎩ " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "i1 = smp.integrate(eq, (t, 0, .25))\n", "i1" ] }, { "cell_type": "code", "execution_count": 13, "id": "0ea4f33f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\begin{cases} \\frac{i}{2 \\pi k} - \\frac{i e^{- 1.5 i \\pi k}}{2 \\pi k} & \\text{for}\\: k \\neq 0 \\\\0.25 & \\text{otherwise} \\end{cases}$" ], "text/plain": [ "⎧ -1.5⋅ⅈ⋅π⋅k \n", "⎪ ⅈ ⅈ⋅ℯ \n", "⎪───── - ───────────── for k ≠ 0\n", "⎨2⋅π⋅k 2⋅π⋅k \n", "⎪ \n", "⎪ 0.25 otherwise\n", "⎩ " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "i2 = smp.integrate(eq, (t, .75, 1))\n", "i2" ] }, { "cell_type": "code", "execution_count": 14, "id": "00ca5455", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\frac{i e^{- 1.5 i \\pi k}}{2 \\pi k} + \\frac{i e^{- 0.5 i \\pi k}}{2 \\pi k}$" ], "text/plain": [ " -1.5⋅ⅈ⋅π⋅k -0.5⋅ⅈ⋅π⋅k\n", " ⅈ⋅ℯ ⅈ⋅ℯ \n", "- ───────────── + ─────────────\n", " 2⋅π⋅k 2⋅π⋅k " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "itotal = i1.args[0].args[0] + i2.args[0].args[0]\n", "itotal" ] }, { "cell_type": "code", "execution_count": 15, "id": "22915fc3", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{\\sin{\\left(\\frac{\\pi k}{2} \\right)} - \\sin{\\left(\\frac{3 \\pi k}{2} \\right)} + i \\cos{\\left(\\frac{\\pi k}{2} \\right)} - i \\cos{\\left(\\frac{3 \\pi k}{2} \\right)}}{2 \\pi k}$" ], "text/plain": [ " ⎛π⋅k⎞ ⎛3⋅π⋅k⎞ ⎛π⋅k⎞ ⎛3⋅π⋅k⎞\n", "sin⎜───⎟ - sin⎜─────⎟ + ⅈ⋅cos⎜───⎟ - ⅈ⋅cos⎜─────⎟\n", " ⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠\n", "─────────────────────────────────────────────────\n", " 2⋅π⋅k " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ff = smp.simplify(itotal.rewrite(smp.sin))\n", "ff" ] }, { "cell_type": "code", "execution_count": 16, "id": "b3493e72", "metadata": {}, "outputs": [], "source": [ "from sympy.simplify.fu import TR9 # combine trig sums to products" ] }, { "cell_type": "code", "execution_count": 17, "id": "cdcb7774", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\frac{\\left(-1\\right)^{k} \\sin{\\left(\\frac{\\pi k}{2} \\right)}}{\\pi k}$" ], "text/plain": [ " k ⎛π⋅k⎞ \n", "-(-1) ⋅sin⎜───⎟ \n", " ⎝ 2 ⎠ \n", "────────────────\n", " π⋅k " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "TR9(ff)" ] }, { "cell_type": "markdown", "id": "6cc79d78", "metadata": {}, "source": [ "The even integers inbetween have no effect as $ sin ( \\frac{\\pi ( 2k ) }{2}) = 0 $ and we also note that for odd k that the expression $ -(-1)^k $ is always equal to 1 so the only terms we need to consider is for when k is odd which we can represent by $ 2k - 1 $ and if we only consider those numbers then we have the following.\n", "\n", "$$ - \\frac{\\left(-1\\right)^{2k-1} \\sin{\\left(\\frac{\\pi (2k-1)}{2} \\right)}}{\\pi (2k-1)} $$\n", "\n", "which should simplify to:\n", "\n", "$$ C_{2k-1}= \\frac{(-1)^{k-1} }{\\pi (2k - 1)} $$\n", "\n", "when k is odd and zero otherwise.\n", "\n", "(**Note:** This yields only half the value of what we expect on the frequency distribution because we have to sum up both sides of $C_k$ and $C_{-k}$ which doubles the value.)" ] }, { "cell_type": "markdown", "id": "dd322e83", "metadata": {}, "source": [ "Now lets look at a function without jump discontinuities but has discontinuities in the first derivative." ] }, { "cell_type": "code", "execution_count": 18, "id": "16032329", "metadata": {}, "outputs": [], "source": [ "def fn(t):\n", " if t < 0.5:\n", " return 2*t\n", " else:\n", " return 1-2*(t-.5)" ] }, { "cell_type": "code", "execution_count": 19, "id": "06de8373", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0,1, num=200)\n", "ff = np.vectorize(fn)\n", "y = ff(x)\n", "ax = plt.gca()\n", "ax.grid()\n", "plt.plot(x,y)" ] }, { "cell_type": "code", "execution_count": 20, "id": "89293d8a", "metadata": {}, "outputs": [], "source": [ "fourier = Fourier(fn)" ] }, { "cell_type": "code", "execution_count": 21, "id": "9063d3eb", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fourier.plot_frequencies()" ] }, { "cell_type": "code", "execution_count": 22, "id": "235dfec3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fourier.plot_reconstructions(max_harmonics = [4,6,10,16,30, 60])" ] }, { "cell_type": "markdown", "id": "dc5d27a3", "metadata": {}, "source": [ "I might look at if I can cirumvent Gibbs phenomena for a square wave by removing the jump discontinuities and replacing them with very steep, yet finite, slope." ] }, { "cell_type": "code", "execution_count": null, "id": "4746e715", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }