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Discrete Fourier transform matrix


A = dftmtx(n)


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 vector, x, computes the discrete Fourier transform of x. In other words, y = A*x is the same as y = fft(x).

The inverse discrete Fourier transform matrix is

Ai = conj(dftmtx(n))/n


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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);

ans =


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dftmtx takes the FFT of the identity matrix to generate the transform matrix.

See Also


Introduced before R2006a

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