% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Epage 
% 
%-----

close all; clc; clear; 

X = [ 1, 2, 1; 0, 1, 1; 2, 1, 2 ];

% Check that the expression conj(dftmtx(N))/sqrt(N) generates the book's matrix W: 
%
%N   = 40;
N = size(X,1); 
W_N = exp( -i * 2 * pi / N );
pwr = ( 0:(N-1) )';
w_n_exponents = pwr * (pwr');
WHhat_no_N = W_N .^ w_n_exponents; % this is W^H (without the factor of 1/sqrt(N))
What_no_N = conj( WHhat_no_N ); % this is W without the factor of 1/sqrt(N) 

WH_no_N = dftmtx(N); % this is W^H (without the factor of 1/sqrt(N))
W_no_N = conj(dftmtx(N)); % this is W without the factor of 1/sqrt(N) 

% check that the two matrices are the same: 
norm( What_no_N - W_no_N ) 

% put in the denominators: 
WH = WH_no_N/sqrt(N);
W  = W_no_N/sqrt(N); 

% now compute the DFT (using matrix multiplications):
% 
Y = WH * X * WH;
Y