Discrete Fourier transform matrix
A discrete Fourier transform
matrix is a complex matrix of values around the unit circle,
whose matrix product with a vector computes the discrete Fourier transform
of the vector.
A = dftmtx(n) returns the n-by-n complex
matrix A that, when multiplied into a length n column
y = A*x
computes the discrete Fourier transform of x.
The inverse discrete Fourier
transform matrix is
Ai = conj(dftmtx(n))/n
In practice, the discrete Fourier transform is computed more
efficiently and uses less memory with an FFT algorithm
x = 1:256;
y1 = fft(x);
than by using the Fourier transform matrix.
n = length(x);
y2 = x*dftmtx(n);
dftmtx takes the FFT of the identity matrix
to generate the transform matrix.
convmtx | fft
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