Communications Toolbox

Discrete Fourier Transform

The discrete Fourier transform is an important tool in digital signal processing. This toolbox offers these tools to help you process discrete Fourier transforms:

• fft, which transforms a Galois vector

• ifft, which inverts the discrete Fourier transform on a Galois vector

• dftmtx, which returns a Galois array that you can use to perform or invert the discrete Fourier transform on a Galois vector

In all cases, the vector being transformed must be a Galois vector of length 2^m-1 in the field GF(2^m). The examples below illustrate the use of these functions. You can check, using the isequal function, that y equals y1, z equals z1, and z equals x.

m = 4;
x = gf(randint(2^m-1,1,2^m),m); % A vector to transform
alph = gf(2,m);
dm = dftmtx(alph);
idm = dftmtx(1/alph);
y = dm*x; % Transform x using the result of dftmtx.
y1 = fft(x); % Transform x using fft.
z = idm*y; % Recover x using the result of dftmtx(1/alph).
z1 = ifft(y1); % Recover x using ifft.

Tip   If you have many vectors that you want to transform (in the same field), then it might be faster to use dftmtx once and matrix multiplication many times, instead of using fft many times.

Convolution

Polynomials over Galois Fields

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