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How to Plot a Fourier Series?

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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.

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Accepted Answer

Alan Stevens
Alan Stevens on 24 Oct 2020
Edited: Alan Stevens on 24 Oct 2020
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

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