Discrete Fourier transform
fft(x) is the discrete
Fourier transform (DFT) of the Galois vector
x is in the Galois field GF(2m),
the length of
x must be 2m-1.
Set the order of the Galois field. Because
x is in the Galois field (
), the length of
x must be
m = 4; n = 2^m-1;
Generate a random GF vector.
x = gf(randi([0 2^m-1],n,1),m);
Perform the Fourier transform.
y = fft(x);
Invert the transform.
z = ifft(y);
Confirm that the inverse transform
ans = logical 1
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(2m), where m is an
integer between 1 and 8.
x is a column vector,
dftmtx to the primitive element of the
Galois field and multiplies the resulting matrix by