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.
where k and l vary from 1 to N.
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 N.
Finally fftcc performs a complex to complex transform, with
both input and output being of length N.