Discrete Fourier transform matrix
a = dftmtx(n)
In practice, it is more efficient to compute the discrete Fourier transform with the FFT than with the DFT matrix. The FFT also uses less memory. The two procedures give the same result.
x = 1:256; y1 = fft(x); n = length(x); y2 = x*dftmtx(n); norm(y1-y2)
ans = 9.3125e-12
n— Discrete Fourier transform length
Discrete Fourier transform length, specified as an integer.
a— Discrete Fourier transform matrix
Discrete Fourier transform matrix, returned as a matrix.
A discrete Fourier transform matrix is a complex
matrix whose matrix product with a vector computes the discrete Fourier transform of the
dftmtx takes the FFT of the identity matrix to generate the
For a column vector
y = dftmtx(n)*x
y = fft(x,n). The inverse discrete Fourier transform matrix is
ainv = conj(dftmtx(n))/n