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Fast Fourier Transform

The fft package is a wrapper of the C language version of PocketFFT library designed to support FFT of real to complex and complex to real (arrays).

The result of a real-to-complex transform, because of mathematical symmetry of the result, is stored in the original input array rather than 2x the space.

The output is the two real values bracketing the complex pairs of conjugate negative frequencies: r0 r1 i1 r2 i2 r3 i3 ... rx

where r0 + i0 is the first complex result, r1 - i1 is the second, and so on until rx + i0 (where x is n/2) is the last. (Note the minus signs.)

The positive frequencies are the same as the negative frequencies in reverse order. See the reference for FFTW for further examples of embeddings.