Calculating Fourier Series Coefficients

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.

[omar seraj]

How to plot in Fourier series given a time interval -1.5 to 2.5I need a step by step answer to this problem please

Answer 1

[Rick Rosson]

>> doc fft
>> doc real
>> doc imag

http://en.wikipedia.org/wiki/Fourier_series

Answer 2

[Youssef Khmou]

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

Answer 3

[Kamal Kaushal]

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');

Answer 4

[Hemang Mehta]

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');

[Aaron Vargas]

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

[Rik]

Comment posted as flag by Hariharan Hariharan:

need the flowof code for case study

Answer 5

[Sikha ranjith kumar]

x(t)=cos(50t)