Output of Fourier Transforms of Complex Data

The output of fftc1 is arranged as follows. The first half of the output array represents the positive frequencies $0 \leq i \leq N/2$. The index $i$ then wraps around to $-N/2$ and begins ascending from there. (Remember that $F_{N/2}$ and $F_{-N/2}$ are the same point.) Bearing in mind that the array contains alternating real and imaginary components, the input and output arrays look like:

$$Input array = I[2 N] = \{Re(f_{x1}),Im(f_{x1}),Re(f_{x2}),...,Im(f_{xN})\}$$ (7)

$$Output array = O[2 N] = \{Re(F_0),Im(F_0),Re(F_1),...,Re(F_{N/2}),Im(F_{N/2}),Re(F_{-N/2+1}),...,Im(F_{-1})\}$$ (8)

Remember that $I$ and $O$ are actually the same array because the output data are written over the original input array. The output of fftcn is arranged analogously to fftc1. Each dimension goes from $0$ to $N/2$ and then from $-N/2$ up to $-1$ and the whole array alternates between real and imaginary parts.

To do an inverse Fourier transform simply arrange the values $F_k$ as described here. If the array $f[\;]$ was produced as output of the FFTEASY routines then it is already arranged correctly to be put back in for the inverse Fourier transform.