Module rgsl::fft::real_radix2

This section describes radix-2 FFT algorithms for real data. They use the Cooley-Tukey algorithm to compute in-place FFTs for lengths which are a power of 2.

Functions

backward	This function computes the inverse or backwards in-place radix-2 FFT of length n and stride stride on the half-complex sequence data stored according the output scheme used by gsl_fft_real_radix2. The result is a real array stored in natural order.
inverse	This function computes the inverse or backwards in-place radix-2 FFT of length n and stride stride on the half-complex sequence data stored according the output scheme used by gsl_fft_real_radix2. The result is a real array stored in natural order.
transform	This function computes an in-place radix-2 FFT of length n and stride stride on the real array data. The output is a half-complex sequence, which is stored in-place. The arrangement of the half-complex terms uses the following scheme: for k < n/2 the real part of the k-th term is stored in location k, and the corresponding imaginary part is stored in location n-k. Terms with k > n/2 can be reconstructed using the symmetry z_k = z*_{n-k}. The terms for k=0 and k=n/2 are both purely real, and count as a special case. Their real parts are stored in locations 0 and n/2 respectively, while their imaginary parts which are zero are not stored.
unpack	This function converts halfcomplex_coefficient, an array of half-complex coefficients as returned by gsl_fft_real_radix2_transform, into an ordinary complex array, complex_coefficient. It fills in the complex array using the symmetry z_k = z_{n-k}* to reconstruct the redundant elements. The algorithm for the conversion is,