How to Plot a Fourier Series?

Hi,

I was given a half range expansion function f(x) = 0, 0<x<2 and f(x) = 1, <2<x<4.

I was asked to solve for the Fourier cosine series and Fourier sine series and then plot each.

I solved by hand:

Fourier Cosine Series:

a0 = 1/2

an = -2/(n*pi)*sin((n*pi)/2)

f(x) = 1/2 + sum(an*cos((n*pi*x)/4)) from n =1 to infinity

Fourier Sine Series:

bn = [2/(n*pi)]*[(-1)^(n+1) + cos((n*pi)/2)]

f(x) = sum(bn*sin((n*pi*x)/4))

I'm fairly new to Matlab and very unexperienced, where I'm having dificulty is plotting these functions against x, say x = [-24 24] and n=1:1:50 or until square waves appear. I gained some experience plotting their partial sums using fplot, but that approach does not appear to work here. It isn't feasible to plot the 50th partial sum. I've seen more arrayfun usage online, but I do not understand it whatsoever.

Any help and explanation would be greatly appreciated. Thanks in advance.

Answer 1

[Alan Stevens]

Here's the cosine version. You can add the sin version and play with different ranges for n:

x = -24:0.1:24;
n = 10;
ycos = fcos(x,n);
plot(x,ycos),grid
xlabel('x'),ylabel('cos function')


% Define functions
function f = fcos(x,n)
         
         f = zeros(1,numel(x));
         f = 1/2;
         for i = 1:n
             an = -2*sin(i*pi/2)/(i*pi);
             f = f + an*cos(i*pi*x/4);
         end

end

This results in

[Alexander McGlone]

Thank you!

Answer 2

[Gabriele Bunkheila]

If you need a review of the basics on Fourier Analysis, I recommend taking a look at the Fourier Analysis learning module on MATLAB Central File Exchange (including the Sine and Cosine series App captured below).

Answer 3

[Bhavik Jain]

bn=[2/(n*pi)]*[(x^2)^(n+1)+cos((n*pi)/2)]