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FFT Routines

There are three FFT routines, namely:
subroutine fftrc(in,out,sign,n)
subroutine fftcr(in,out,sign,n)
subroutine fftcc(in,out,sign,n)

These perform one-dimensional FFTs. In all cases, `sign` is the sign
of the exponent in the transform (i.e. a `sign` of -1 is conventionally
viewed as a forward transform), and `n` is a power of 2 giving the
length of the (full) sequence. scaling is never performed
(it is up to you to scale at the best time). `In` is the input
array, and `out` is the output array. These routines
evaluate:

where and vary from to .
`Fftrc` transforms a real
sequence (i.e. `in` is a real array) and outputs only the first
complex values. No information is lost because of the conjugate
symmetry of FFTs of real sequences. Conversely `fftcr` takes a
complex sequence of length and produces a real sequence of length .
Finally `fftcc` performs a complex to complex transform, with
both input and output being of length .

*Miriad manager *

2011-08-19