Example2_13.m

% File: Example2_13.m  for Example 2-13

% Plot a Fourier series for square wave.

% This file demonstrates the Fourier Series representation of a
% 50% duty cycle square wave.  That is To=2T. 

clear;

% Time is evaluated (i.e. the waveform is plotted) over the time
% interval [0,10] in increments of t_inc.
% If you wish to observe Gibbs' phenomenon you should decrease the value
% of t_inc to 0.01, and include a large number of harmonics.

t_inc = 0.1;

% Enter the Number of Harmomics to include in the F.S.
fprintf('Enter N, the number of Harmonics to use in the Fourier Series.\n');
N = input('where N is an odd integer: ');
if (rem(N,2) == 0)
  N = N+1;
end;
fprintf('\n\nCalculating....please wait\n');

A = 1;
fo = 0.5;
wo = 2 * pi * fo;
t = 0:t_inc:10;
j = sqrt(-1);

% Evaluate tne complex Fourier coefficients using Eq. (2-119) for n>0
for (n = 1:2:N)
  c(n) = A/(n*pi*j);
end;

fprintf('The complex Fourier coefficients c(n), for n>=0, are:\n')
% The Fourier series coefficient for n=0 is d(1)
d(1) = A/2;
for k = 2:1:N+1
    d(k) = c(k-1);
end
disp(d)

i = 1;                                            
w = zeros(length(t),1);
while (i <= length(t))
  w(i) = A/2;
  for (n = 1:2:N)
    w(i) = w(i) + c(n)*exp(n*wo*t(i)*j) - c(n)*exp(n*wo*t(i)*(-j));
  end;
  i = i+1;
end;

fprintf('See the plot for the waveform generated by the Fourier series.\n')

plot(t,w);
title(['Fourier Series of Square Wave using ',int2str(N),' Harmonics']);
xlabel('t time in seconds');
ylabel('w(t)');