% Example 5-2: Computation of non-square
% time-varying channel transfer matrix Wc 
clear all
K = 4; % Number of time samples (I/O observations)
N = 2; % Number of channel inputs
M = 3; % Number of channel outputs

X = [1 -2  
     3  1  
     7  4  
     2  3]% Input signal matrix
  
Y = [1  4  2
     8 -1  1
     9  3  8
     2  7 -3]% Output signal matrix  
       
[Q, R] = qr(X); % QR-factorize input matrix
Ux = Q % Orthonormal input basis 
Wx = Ux*X % Generalized Fourier coefficients of input
Wy = Ux*Y % Generalized Fourier coefficients of output
Wc_hat = pinv(Wx)*Wy % Channel Transfer Matrix 
Y_hat = X * Wc_hat % Determine estimate of output matrix  
Errornorm = norm(Y-Y_hat,'fro') % Calculate Frobenius
% norm of output signal error matrix