A Matlab script to calculate the discrete Fourier Transform of a signal using matrix multiplication.

DFT_Matrix.m

clear;
clc;

% This is a test

% This x[n] is a simple square pulse centered at the origin
% it can be replaced with any finite-duration signal, as long as
% n is updated to match
x = [ zeros(1,8) ones(1,5) zeros(1,8) ];
n = -10:10;

stepsize = pi/20;

W = -pi:stepsize:pi;

% We have to create the first column of the matrix outside of the
% loop. There may be a better way of doing this, I'm not sure.
matrix = exp(-j*W(1)*n)';

% We build up the matrix by successively concatenating columns
for w = W(2:length(W))
    matrix = [ matrix exp(-j*w*n)' ];
end

% The product of the original signal and the matrix gives the
% Fourier transform of the signal!
transform = x * matrix;

% plot it
subplot(2,1,1);
stem(n,x);
title('x[n]');

subplot(2,1,2);
plot(W, abs(transform));
title('Fourier transform of x[n] (over one period)');