fft - Discrete Fourier transform

Syntax

fft(x) 

Description

fft(x) is the discrete Fourier transform (DFT) of the Galois vector x. If x is in the Galois field GF(2^m), the length of x must be 2^m-1.

Examples

m = 4;
n = 2^m-1;
x = gf(randi([0 2^m-1],n,1),m); % Random vector
y = fft(x); % Transform of x
z = ifft(y); % Inverse transform of y
ck = isequal(z,x) % Check that ifft(fft(x)) recovers x.

The output is

ck =

     1

Limitations

The Galois field over which this function works must have 256 or fewer elements. In other words, x must be in the Galois field GF(2^m), where m is an integer between 1 and 8.

Algorithms

If x is a column vector, fft applies dftmtx to the primitive element of the Galois field and multiplies the resulting matrix by x.

See Also

dftmtx | ifft

How To

• Signal Processing Operations in Galois Fields

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