dftmtx
Discrete Fourier transform matrix
Syntax
Description
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 = 9.6887e-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
y = fft(x,n)
. The inverse discrete Fourier transform matrix
isainv = conj(dftmtx(n))/n
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced before R2006a
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