Asked by omar alblooshi
on 16 Mar 2018

how to plot fourier series in matlab

Answer by Abhishek Ballaney
on 16 Mar 2018

https://in.mathworks.com/help/curvefit/fourier.html

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Answer by Abraham Boayue
on 18 Mar 2018

Edited by Abraham Boayue
on 15 Jun 2018 at 5:21

Here is what your Fourirer series would like if my calculations were made correctly. An attachment of the solution is also included for your reference. Take care for now.

clear variables close all % Fourier series of neither even nor odd function % Decompose f(x) into even (fe) and odd (fo) functions. % fe = (f(x) + f(-x))/2, fo = (f(x) - f(-x))/2 N = 500; L = 4; xd = -L:2*L/(N-1):L; y1 = -1/8*xd.^2; y2 = 1/8*xd.^2; fo = y1.*(-L<=xd & xd<=0) +y2.*(0<=xd & xd<=L); fe = 4-xd.^2/8; f2 = fe + fo; a0 = 10/3; % Generate the fourier series of f(x) y = zeros(1,N); x = []; K = 80; for k = 1:K ck = 1/(pi*k); an = (2*L*(-1).^(k+1))*ck^2; bn = L*(-1).^(k+1)*ck + (2*L*ck^3)*((-1)^k-1); y = y + (an*cos(pi*k/L*xd)+ bn*sin(pi*k/L*xd)); % For fe and fo x = [x;y]; end y = a0 +y; x = a0 +x;

% Color codes s = distinguishable_colors(K); % search this function on mathworks

figure subplot(121) % Plot f(t) plot(xd,f2,'linewidth',2.5,'color',s(1,:)) line(xlim,[0 0],'color',s(6,:),'linewidth',3); line([0 0],ylim,'color',s(6,:)','linewidth',3); ylim([-.5 4]); a= xlabel('\itt\rm (seconds)'); set(a,'fontsize',20); a = ylabel('\itf\rm(\itt\rm)'); set(a,'fontsize',20); a= title('f(t)'); set(a,'fontsize',14); grid

subplot(122) % Plot fouries series of f(t); hold on q = length(x(:,1)); M = 1:q; for i = 1:6:q plot(xd,x(i,:),'linewidth',2.5,'color',s(i,:),'DisplayName',sprintf('S = %1.2f',M(i))) end a= title('Fourier series of f(t)'); set(a,'fontsize',14); a= xlabel('\itt\rm (seconds)'); set(a,'fontsize',20); a = ylabel('\itf\rm(\itt\rm)'); set(a,'fontsize',20); line(xlim,[0 0],'color',s(6,:),'linewidth',3); line([0 0],ylim,'color',s(6,:)','linewidth',3); legend('-DynamicLegend','location','bestoutside'); grid

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Answer by Abraham Boayue
on 18 Mar 2018

The is the solution file, the math is a bit messy, but I assume that you are familiar with the material that you are studying.

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## 2 Comments

## Abraham Boayue (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/388652-how-to-plot-fourier-series-in-matlab#comment_545948

Have you done the integrals to fined the a0, an and bn? If so, what is the expression you got for the fourier series?

## Akira Agata (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/388652-how-to-plot-fourier-series-in-matlab#comment_545955

Regarding the question (1) in the picture, I would recommend try to calculate by hand first, for your better understanding of Fourier transformation of periodic function.

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