dftmtx

Discrete Fourier transform matrix

Syntax

a = dftmtx(n)

Description

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

Examples

The FFT and the DFT Matrix

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 = 6.9611e-12

Input Arguments

n — Discrete Fourier transform length

positive integer

Discrete Fourier transform length, specified as an integer.

Data Types: single | double

Output Arguments

a — Discrete Fourier transform matrix

matrix

Discrete Fourier transform matrix, returned as a matrix.

More About

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.