FFT(G)

NAME
fft - fast fourier transform.

CALLING SEQUENCE
[x]=fft(a,-1)
[x]=fft(a,1)
x=fft(a,-1,dim,incr)
x=fft(a,1,dim,incr)

PARAMETERS

x   : real or complex vector. Real or complex matrix (2-dim fft)

a   : real or complex vector.

dim : integer

incr
    : integer

DESCRIPTION
Short syntax (one or two dimensional fft)

gives a direct transform (the -1 refers to
the sign of the exponent..., NOT to "inverse"), that is
x(k)=sum over m of a(m)*exp(-2i*pi*m*k/n)
for k varying from 0 to n-1 (n=size of vector a).

(known bug fft(x,-1) for x of size 99 infinite loop!
add one or more zeros...)

performs the inverse transform normalized by 1/n.

(fft(fft(.,-1),1) is identity).

When the first argument given to fft is a matrix
a two-dimensional FFT is performed.

Long syntax (multidimensional FFT)
allows to perform an multidimensional fft.

If a is a real or complex vector implicitly indexed by
x1,x2,..,xp i.e. a(x1,x2,..,xp) where x1 lies in
1..dim1, x2 in 1.. dim2,... one gets
a p-dimensional FFT p by calling p times fft as follows
 a1=fft(a ,-1,dim1,incr1)
 a2=fft(a1,-1,dim2,incr2) ...
where dimi is the dimension of the current variable w.r.t which one is integrating and incri is the increment which separates two successive xi elements in a.

In particular,if a is an nxm matrix, x=fft(a,-1) is equivalent to the two instructions:

a1=fft(a,-1,m,1) and x=fft(a1,-1,n,m).

SEE ALSO
corr.