.d@0: d@0: d@0: Next: The 1d Real-data DFT, d@0: Previous: What FFTW Really Computes, d@0: Up: What FFTW Really Computes d@0:
The forward (FFTW_FORWARD) discrete Fourier transform (DFT) of a
d@0: 1d complex array X of size n computes an array Y,
d@0: where:
d@0:
.FFTW_BACKWARD) DFT computes:
d@0: 
.FFTW computes an unnormalized transform, in that there is no coefficient d@0: in front of the summation in the DFT. In other words, applying the d@0: forward and then the backward transform will multiply the input by d@0: n. d@0: d@0:
From above, an FFTW_FORWARD transform corresponds to a sign of
d@0: -1 in the exponent of the DFT. Note also that we use the
d@0: standard “in-order” output ordering—the k-th output
d@0: corresponds to the frequency k/n (or k/T, where T
d@0: is your total sampling period). For those who like to think in terms of
d@0: positive and negative frequencies, this means that the positive
d@0: frequencies are stored in the first half of the output and the negative
d@0: frequencies are stored in backwards order in the second half of the
d@0: output. (The frequency -k/n is the same as the frequency
d@0: (n-k)/n.)
d@0:
d@0:
d@0:
d@0: