5.1 Discrete Fourier Transform

dft(X)

Replaces the columns of a dense complex matrix with their discrete Fourier transforms: if X has n rows,

        n∑-1      √--
X [k,:] :=    e-2πjk -1∕nX[j,:],   k = 0,...,n - 1.
        j=0

idft(X)

Replaces the columns of a dense complex matrix with their inverse discrete Fourier transforms: if X has n rows,

           n∑-1    √--
X [k,:] := 1   e2πjk -1∕nX [j,:],    k = 0,...,n - 1.
         n j=0