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. ${1\over N}$ 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:

$$Out(l)=\sum_{k=1}^N In(k)\exp(\pm j {2\pi\over N} (k-1)(l-1))$$

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 $N/2 + 1$ complex values. No information is lost because of the conjugate symmetry of FFTs of real sequences. Conversely fftcr takes a complex sequence of length $N/2 + 1$ and produces a real sequence of length $N$. Finally fftcc performs a complex to complex transform, with both input and output being of length $N$.