function[Xk]=dft(xn,N)
%Computes Discrete Fourier Transform
%-----------------------------------
%[Xk]=dft(xn,N)
%Xk=DFT coeff.array over 0<=k<=N-1
%xn=N-point finite-duration sequence
%N=Length of DFT
n=[0:1:N-1];          %row vector for n
k=[0:1:N-1];          %row vector for k
WN=exp(-j*2*pi/N);    %Wn factor
nk=n'*k;              %creates a N by N matrix of nk values
WNnk=WN.^nk;          %DFT matrix
Xk=xn*WNnk;           %row vector for DFT coefficients

function[xn]=idft(Xk,N)
%Computes Inverse Discrete Transform
%-----------------------------------
%[xn]=idft(Xk,N)
%xn=N-point sequence over 0<=n<=N-1
%Xk=DFT coeff.array over 0<=k<=N-1
%N=length of DFT
n=[0:1:N-1];