6 Fast Fourier Transform functions.

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This section describes functions from file fft.ct.

6.1 fft

[f] = fft(u; dim)
 fft(u) gives the complex Fast Fourier Transform of u.
   If u's rank is more than one, the transform is computed
   only along the first dimension (many independent 1D
   transforms).

   fft(u,dim) computes the FFT along the specified dimension.
   The first dimension is labeled 1 and so on.

   The forward FFT is defined as

   fft(u)_j = sum(c_k * exp(-i*(j-1)*(k-1)*2*pi/n), k=1..n)

   where i = sqrt(-1).
   
   See also: ifft.
   Error codes:
   -1: First argument not a numeric array
   -2: Second argument not integer
   -3: Second argument out of range
   

6.2 ifft

[f] = ifft(u; dim)
 ifft() is the inverse of fft():

   ifft(u)_j = (1/n) * sum(c_k * exp(i*(j-1)*(k-1)*2*pi/n), k=1..n)

   Differences to fft: sign of i is plus, scale factor 1/n.
   
   See fft.
   Error codes:
   -1: First argument not a numeric array
   -2: Second argument not integer
   -3: Second argument out of range
   

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