Communications Toolbox

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), then the length of x must be 2^m-1.

Examples

m = 4;
n = 2^m-1;
x = gf(randint(n,1,2^m),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.

Algorithm

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

See Also

ifft, dftmtx, Signal Processing Operations in Galois Fields

eyediagram

filter (channel)

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