# HW_2 - 2 For 6.1_1a and 6.1_2 plot the Fourier series...

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Unformatted text preview: 2. For 6.1_1a and 6.1_2, plot the Fourier series approximation using the first 5, 10 and 15 harmonics in MATLAB. Fourier series approximation using first 5 harmonics 1.5 1 0.5 0 -0.5 -1 -1.5 -8 -6 -4 -2 0 2 4 6 8 Fourier series approximation using first 10 harmonics 1.5 1 0.5 0 -0.5 -1 -1.5 -8 -6 -4 -2 0 2 4 6 8 Fourier series approximation using first 15 harmonics 1.5 1 0.5 0 -0.5 -1 -1.5 -8 -6 -4 -2 0 2 4 6 8 Matlab code: N_harmonics = 5; %number of harmonics t = -9:.001:9; %set time interval and sampling x = zeros(size(t)); %initialize approximation %perform loop summation for k=1:N_harmonics x = x+(4/pi)*[((-1)^(k-1))/(2*k-1)]*cos((2*k-1)*0.5*pi*t); end figure; plot(t,x); axis([-9 9 -1.5 1.5]); title('Fourier series approximation using first 5 harmonics'); Fourier series approximation using first 5 harmonics 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3pi -2pi -pi 0 pi 2pi 3pi Fourier series approximation using first 10 harmonics 1 0.8 0.6 0.4 0.2 0 -3pi -2pi -pi 0 pi 2pi 3pi Fourier series approximation using first 15 harmonics 1 0.8 0.6 0.4 0.2 0 -3pi -2pi -pi 0 pi 2pi 3pi Matlab code: N_harmonics = 5; %number of harmonics t = -3*pi:.001:3*pi; %set time interval and sampling y = 0.504*ones(size(t)); %initialize approximation %perform loop summation for n=1:N_harmonics y = y+0.504*2/(1+16*n^2)*(cos(2*n*t)-4*n*sin(2*n*t)); end figure; plot(t,y); set(gca,'XTick',-3*pi:pi:3*pi) set(gca,'XTickLabel',{'-3pi','-2pi','-pi','0', 'pi','2pi','3pi'}) axis([-3*pi 3*pi 0 1.2]); title('Fourier series approximation using first 5 harmonics'); ...
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HW_2 - 2 For 6.1_1a and 6.1_2 plot the Fourier series...

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