{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "# Compute the Discrete Fourier Transform of the sequence of numbers l\n", "def dft(l):\n", " N=len(l)\n", " output=[]\n", " k=0\n", " while k<=N-1:\n", " n=0\n", " sum=0\n", " while n<=N-1:\n", " sum=sum+l[n]*e^(-I*2*pi/N*k*n)\n", " n=n+1\n", " output.append(sum)\n", " k=k+1\n", " return output" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Compute the DFT of the sequence a, but just print the norms of \n", "# the complex numbers\n", "def norm_dft(a):\n", " u=dft(a)\n", " output=[]\n", " for v in u:\n", " x=N(v.abs())\n", " if x<0.001:\n", " x=0\n", " output.append(x)\n", " return output" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "f=piecewise([((0,2), 0), ((2,3), 1), ((3,5),0), ((5,6),1), ((6,8),0), ((8,9),1),((9,11),0)])" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(0,11)) # This is a function defined on [0,11], but with period 3" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(0,11))+plot(fourier_approx(f,15,11,x),(x,0,11),color='red')+plot(fourier_approx(f,4,11,x),(x,0,11),color='green')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# This function gives the coefficients in the Fourier series for f.\n", "# Prints out [k:a_k,b_k,f_k] where a_k is the coefficient of cosine,\n", "# b_k is the coefficient of sine, and f_k is the frequency\n", "#\n", "def fourier_exp(f,n,length): #compute series from k=0 to k=n\n", " i=1\n", " L=length/2\n", " a0=f.fourier_series_cosine_coefficient(0)/2\n", " output=[[0,':',a0,0,0]]\n", " while i<=n:\n", " a=N(f.fourier_series_cosine_coefficient(i))\n", " if abs(a)<0.0001:\n", " a=0\n", " b=N(f.fourier_series_sine_coefficient(i))\n", " if abs(b)<0.0001:\n", " b=0\n", " output.append([i,':',a,b,i/L*pi])\n", " i=i+1\n", " return output\n", " " ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[0, ':', 3/11, 0, 0],\n", " [1, ':', -0.128306329010999, 0, 2/11*pi],\n", " [2, ':', -0.158149502028013, 0, 4/11*pi],\n", " [3, ':', -0.293619439869413, 0, 6/11*pi],\n", " [4, ':', 0.388353062244215, 0, 8/11*pi],\n", " [5, ':', 0.0390335710237439, 0, 10/11*pi],\n", " [6, ':', -0.0325279758531199, 0, 12/11*pi],\n", " [7, ':', -0.221916035568123, 0, 14/11*pi],\n", " [8, ':', 0.110107289951030, 0, 16/11*pi],\n", " [9, ':', 0.0351443337840029, 0, 18/11*pi],\n", " [10, ':', 0.0128306329010999, 0, 20/11*pi],\n", " [11, ':', 0, 0, 2*pi],\n", " [12, ':', -0.0106921940842499, 0, 24/11*pi],\n", " [13, ':', -0.0243306926196943, 0, 26/11*pi],\n", " [14, ':', -0.0629184514005885, 0, 28/11*pi],\n", " [15, ':', 0.103560816598457, 0, 30/11*pi]]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fourier_exp(f,15,11)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [], "source": [ "# The gives the Fourier approximation function defined using a sum\n", "# from k=0 to k=n\n", "# Here \"length\" is the length of the original interval on which f\n", "# is defined.\n", "#\n", "def fourier_approx(f,n,length,x):\n", " list=fourier_exp(f,n,length)\n", " temp=list[0][2]\n", " i=1\n", " while i<=n:\n", " freq=list[i][4]\n", " A=list[i][2]\n", " B=list[i][3]\n", " temp=temp+A*cos(freq*x)+B*sin(freq*x)\n", " i=i+1\n", " return temp" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "f=piecewise([ ((0,1),0),((1,2),1 ) ])" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(0,2))" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(0,2))+plot(fourier_approx(f,1,2,x),(x,0,2),color='red')\n" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(0,2))+plot(fourier_approx(f,5,2,x),(x,0,2),color='red')\n" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[3.00000000000000,\n", " 0.715370323453430,\n", " 0.918985947228995,\n", " 1.83083002600377,\n", " 2.68250706566236,\n", " 0.309721467890568,\n", " 0.309721467890572,\n", " 2.68250706566236,\n", " 1.83083002600377,\n", " 0.918985947228996,\n", " 0.715370323453425]" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f=[0,0,1,0,0,1,0,0,1,0,0] #Here N=11 and s=3 \n", "norm_dft(f) #Get spikes in F near 11/3 and 2*(11/3) " ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[18.0000000000000,\n", " 0.668419798944521,\n", " 0.673736120718789,\n", " 0.682791329343547,\n", " 0.695895486700944,\n", " 0.713521983562587,\n", " 0.736355241089115,\n", " 0.765366864730180,\n", " 0.801937735804843,\n", " 0.848058351891489,\n", " 0.906669817410423,\n", " 0.982273197446115,\n", " 1.08208834612854,\n", " 1.21844027553862,\n", " 1.41421356237310,\n", " 1.71723086396957,\n", " 2.24697960371747,\n", " 3.40954570983426,\n", " 8.04691719426355,\n", " 15.1010780357509,\n", " 3.51351878929970,\n", " 1.84775906502257,\n", " 1.17190265282955,\n", " 0.798431468126536,\n", " 0.554958132087373,\n", " 0.377365428858003,\n", " 0.235750464926204,\n", " 0.113569091696766,\n", " 0,\n", " 0.113569091696802,\n", " 0.235750464926220,\n", " 0.377365428857995,\n", " 0.554958132087371,\n", " 0.798431468126585,\n", " 1.17190265282957,\n", " 1.84775906502257,\n", " 3.51351878929973,\n", " 15.1010780357508,\n", " 8.04691719426358,\n", " 3.40954570983431,\n", " 2.24697960371745,\n", " 1.71723086396955,\n", " 1.41421356237310,\n", " 1.21844027553866,\n", " 1.08208834612850,\n", " 0.982273197446101,\n", " 0.906669817410410,\n", " 0.848058351891429,\n", " 0.801937735804848,\n", " 0.765366864730180,\n", " 0.736355241089097,\n", " 0.713521983562637,\n", " 0.695895486700941,\n", " 0.682791329343491,\n", " 0.673736120718728,\n", " 0.668419798944479]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f=[0,0,1,0,0,1,0,0,1]\n", "f=f+f+f # Here N=56 and s=3. Get spikes in F near\n", "f=f+f+[0,0] # 56/3 and 2*(56/3)\n", "norm_dft(f)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_plot(f)+list_plot(norm_dft(f),color='red')" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[0, ':', 3/11, 0, 0],\n", " [1, ':', -0.128306329010999, 0, 2/11*pi],\n", " [2, ':', -0.158149502028013, 0, 4/11*pi],\n", " [3, ':', -0.293619439869413, 0, 6/11*pi],\n", " [4, ':', 0.388353062244215, 0, 8/11*pi],\n", " [5, ':', 0.0390335710237439, 0, 10/11*pi],\n", " [6, ':', -0.0325279758531199, 0, 12/11*pi],\n", " [7, ':', -0.221916035568123, 0, 14/11*pi],\n", " [8, ':', 0.110107289951030, 0, 16/11*pi],\n", " [9, ':', 0.0351443337840029, 0, 18/11*pi],\n", " [10, ':', 0.0128306329010999, 0, 20/11*pi],\n", " [11, ':', 0, 0, 2*pi],\n", " [12, ':', -0.0106921940842499, 0, 24/11*pi],\n", " [13, ':', -0.0243306926196943, 0, 26/11*pi],\n", " [14, ':', -0.0629184514005885, 0, 28/11*pi],\n", " [15, ':', 0.103560816598457, 0, 30/11*pi],\n", " [16, ':', 0.0121979909449200, 0, 32/11*pi],\n", " [17, ':', -0.0114804620658070, 0, 34/11*pi],\n", " [18, ':', -0.0863006804987144, 0, 36/11*pi],\n", " [19, ':', 0.0463609641899073, 0, 38/11*pi],\n", " [20, ':', 0.0158149502028013, 0, 40/11*pi],\n", " [21, ':', 0.00610982519099997, 0, 42/11*pi],\n", " [22, ':', 0, 0, 4*pi],\n", " [23, ':', -0.00557853604395649, 0, 46/11*pi],\n", " [24, ':', -0.0131791251690011, 0, 48/11*pi],\n", " [25, ':', -0.0352343327843296, 0, 50/11*pi]]" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f=piecewise([((0,2), 0), ((2,3), 1), ((3,5),0), ((5,6),1), ((6,8),0), ((8,9),1),((9,11),0)])\n", "fourier_exp(f,25,11) #N=11, s=3: note the biggest contributions are\n", " #around k=11/3, 2*(11/3), 3*(11/3), 4*(11/3) and so on" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Here we show f in blue, the Fourier approx in red, and the \n", "#\"largest coefficient\" terms of the Fourier approximation in green\n", "plot(f,(0,11))+plot(fourier_approx(f,25,11,x),(0,11),color='red')+plot(3/11-0.29*cos(6/11*pi*x)+0.388*cos(8/11*pi*x)-0.22*cos(14/11*pi*x)+0.11*cos(16/11*pi*x),(0,11),color='green')" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Example of a sum of cosine and sine functions with different periods\n", "plot(cos(3*x)+sin(5*x)+6*cos(x),(0,20))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.7", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }