%% Ncossinmat4
%% function that returns the matrix to produce "Fourier"  cosine-sine coefficients
%% this function is the same as Ncossinmat and Ncossinmat2 

function A = Ncossinmat3(N)

% test of even or odd
% even = 1 if N is even and even =0 if N is odd. Note the use of ~.
even = ~rem(N,2);
n = fix((N-1)/2);

%Construct matrix of sample points. Note the use of ' 
t = (2*pi/N)*(0:1:(N-1))';
jt = t*(1:n);

% the sytement uses vectorized calculation on an entire matrix
A = ones(N,1);
A = [A,cos(jt)];
if even A = [A, cos((N/2)*t)]; end;
A = [A,sin(jt)];