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.
  
  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

eyediagram

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