# Calculating Fourier Series Coefficients

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Jay Mayle on 6 Mar 2013
Commented: Aaron Vargas on 9 Dec 2020
I am trying to compute the trigonometric fourier series coefficients of a periodic square wave time signal that has a value of 2 from time 0 to 3 and a value of -12 from time 3 to 6. It then repeats itself. I am trying to calculate in MATLAB the fourier series coefficients of this time signal and am having trouble on where to begin.
The equation is x(t) = a0 + sum(bk*cos(2*pi*f*k*t)+ck*sin(2*pi*f*k*t))
The sum is obviously from k=1 to k=infinity.
a0, bk, and ck are the coefficients I am trying to find. Thanks for the help.

Youssef Khmou on 6 Mar 2013
Edited: Youssef Khmou on 6 Mar 2013
hi Jay , computing a0 bk and ck is bout theory i think, anyway try :
You have first to construct the original signal "Square(t)" so as to compare it with Fourier approximation :
clear , close all;
Fs=60;
t=0:1/Fs:20-1/Fs;
y=square(t,50);
y(y>0)=2;
y(y<0)=-12;
figure, plot(t,y);
axis ([0 20 -20 10])
% Fourier Series
a0=0;
Fy=zeros(size(t));
N=10;
for n=1:2:N
Fy=Fy+(4/n*pi)*sin(2*pi*n*t/(2*pi));
end
hold on,
plot(t,Fy,'r')
legend(' Square ','Fourier Approx');
Try now to to compute an, and bn and increase the number of iterations N and conclude
You have also to adjust the amplitudes

Rick Rosson on 6 Mar 2013
Edited: Rick Rosson on 6 Mar 2013
>> doc fft
>> doc real
>> doc imag

Kamal Kaushal on 1 Mar 2020
clear , close all;
Fs=60;
t=0:1/Fs:20-1/Fs;
y=square(t,50);
y(y>0)=2;
y(y<0)=-12;
figure, plot(t,y);
axis ([0 20 -20 10])
% Fourier Series
a0=0;
Fy=zeros(size(t));
N=10;
for n=1:2:N
Fy=Fy+(4/n*pi)*sin(2*pi*n*t/(2*pi));
end
hold on,
plot(t,Fy,'r')
legend(' Square ','Fourier Approx');

Hemang Mehta on 23 Oct 2020
clear , close all;
Fs=60;
t=0:1/Fs:20-1/Fs;
y=square(t,50);
y(y>0)=2;
y(y<0)=-12;
figure, plot(t,y);
axis ([0 20 -20 10])
% Fourier Series
a0=0;
Fy=zeros(size(t));
N=10;
for n=1:2:N
Fy=Fy+(4/n*pi)*sin(2*pi*n*t/(2*pi));
end
hold on,
plot(t,Fy,'r')
legend(' Square ','Fourier Approx');

#### 1 Comment

Aaron Vargas on 9 Dec 2020
hello , is there any chance that you can explain to me the variables and how it works ? im stuck in a homework for college