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dftmtx

Discrete Fourier transform matrix

Syntax

a = dftmtx(n)

Description

example

a = dftmtx(n) returns an n-by-n complex discrete Fourier transform matrix.

Examples

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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);

norm(y1-y2)
ans = 9.3125e-12

Input Arguments

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Discrete Fourier transform length, specified as an integer.

Data Types: single | double

Output Arguments

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Discrete Fourier transform matrix, returned as a matrix.

More About

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Discrete Fourier Transform Matrix

A discrete Fourier transform matrix is a complex matrix whose matrix product with a vector computes the discrete Fourier transform of the vector. dftmtx takes the FFT of the identity matrix to generate the transform matrix.

For a column vector x,

y = dftmtx(n)*x
is the same as y = fft(x,n). The inverse discrete Fourier transform matrix is
ainv = conj(dftmtx(n))/n

See Also

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Introduced before R2006a