Does Octave contain Fast-Fourier Transforms built in?

[Francesco Potorti`]

I wrote some functions for that purpose:

----------- spectre.m ---------------
function A = spectre(x, n)

# Given a vector X, compute its one-sided power spectre in N points plus
# the null frequency by repeatedly applying the fft to overlapping chunks of
# 2*N points.  
# Faster if N is a power of 2.  The variance of each element in the computed
# vector is approximately equal to avg*N/length(X), where avg is the
# element's average.  Gives a vector of length N+1. 

  if (length(x) < 2*n)
    x = postpad (x, 2*n);
  endif
  A = 0;
  iterations = max (1, floor(length(x)/n)-1);
  for i = 0:iterations-1
    a = fft (x(i*n+1:(i+2)*n));
    A = A + abs(a(1:n+1)).^2;
    A = A + abs(flipud(fliplr(postpad(a(n+1:2*n), n+1)))).^2;
  endfor
  A = A / n^2;
endfunction


---------------- autocov.m --------------------
function A = autocov(x)

# Given a vector X, computes a vector of the same shape, whose length
# is one less than the argument, representing the autocovariance of X.

  A = x - mean(x);
  A = fftconv(A, fliplr(flipud(A)));
  A = A(length(x) : 2*length(x)-1);
  A = A / length(x);
endfunction


---------------------- autocorr.m --------------------
function A = autocorr(x)

# Given a vector X, computes a vector of the same shape, whose length
# is one less than the argument, representing the autocorrelation of X.
# The autocorrelation is simply the normalised autocovariance.

  A = autocov(x);
  A = A / A(1);
endfunction