DFT

function [Xk] = dft(xn,N)
% Compute DFT
% Xk = DFT coeff. array over 0<=k<=N-1;
% xn = N-point finite-duration sequence;
% N = Length of DFT
n = [0:1:N-1];
k = [0:1:N-1];
WN = exp(-1j*2*pi/N);
nk = n'*k;
WNnk = WN.^nk;
Xk = xn * WNnk;
end

function [xn] = idft(Xk,N)
% Compute DFS
% Xk = N-point sequence over 0<=k<=N-1;
% xn = One period of periodic signal over 0<=n<=N-1;
% N = length of DFT
n = [0:1:N-1];
k = [0:1:N-1];
WN = exp(-1j*2*pi/N);
nk = n'*k;
WNnk = WN.^(-nk);
xn = (Xk * WNnk)/N;
end