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dftmtx

Discrete Fourier transform matrix

Syntax

Description

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.

The inverse discrete Fourier transform matrix is

Examples

In practice, the discrete Fourier transform is computed more efficiently and uses less memory with an FFT algorithm

than by using the Fourier transform matrix.

Algorithm

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

See Also

convmtx, fft


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