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Chris@42:The forward (FFTW_FORWARD) discrete Fourier transform (DFT) of a
Chris@42: 1d complex array X of size n computes an array Y,
Chris@42: where:
Chris@42:
.FFTW_BACKWARD) DFT computes:
Chris@42: 
.FFTW computes an unnormalized transform, in that there is no coefficient Chris@42: in front of the summation in the DFT. In other words, applying the Chris@42: forward and then the backward transform will multiply the input by Chris@42: n. Chris@42:
Chris@42: Chris@42:From above, an FFTW_FORWARD transform corresponds to a sign of
Chris@42: -1 in the exponent of the DFT. Note also that we use the
Chris@42: standard “in-order” output ordering—the k-th output
Chris@42: corresponds to the frequency k/n (or k/T, where T
Chris@42: is your total sampling period). For those who like to think in terms of
Chris@42: positive and negative frequencies, this means that the positive
Chris@42: frequencies are stored in the first half of the output and the negative
Chris@42: frequencies are stored in backwards order in the second half of the
Chris@42: output. (The frequency -k/n is the same as the frequency
Chris@42: (n-k)/n.)
Chris@42: