This is a python version of the logarithmic FFT code FFTLog as presented in Appendix B of [Hamilton_2000] and published at casa.colorado.edu/~ajsh/FFTLog.
A simple f2py-wrapper (fftlog) can be found on github.com/prisae/fftlog. Tests have shown that fftlog is a bit faster than pyfftlog, but pyfftlog is easier to implement, as you only need NumPy and SciPy, without the need to compile anything.
I hope that FFTLog will make it into SciPy in the future, which will make this project redundant.
Be aware that pyfftlog has not been tested extensively. It works fine for the attached test, which is the test from the original code, and my use case, which is pyfftlog.fftl with mu=0.5 (sine-transform), q=0 (unbiased), k=1, kropt=1, and tdir= (forward). Please let me know if you encounter any issues.
FFTLog is a set of fortran subroutines that compute the fast Fourier or Hankel (= Fourier-Bessel) transform of a periodic sequence of logarithmically spaced points.
FFTLog can be regarded as a natural analogue to the standard Fast Fourier Transform (FFT), in the sense that, just as the normal FFT gives the exact (to machine precision) Fourier transform of a linearly spaced periodic sequence, so also FFTLog gives the exact Fourier or Hankel transform, of arbitrary order m, of a logarithmically spaced periodic sequence.
FFTLog shares with the normal FFT the problems of ringing (response to sudden steps) and aliasing (periodic folding of frequencies), but under appropriate circumstances FFTLog may approximate the results of a continuous Fourier or Hankel transform.
The FFTLog algorithm was originally proposed by [Talman_1978].
For the full documentation, see casa.colorado.edu/~ajsh/FFTLog.
| [Hamilton_2000] | (1, 2) Hamilton, A. J. S., 2000, Uncorrelated modes of the non-linear power spectrum: Monthly Notices of the Royal Astronomical Society, 312, pages 257-284; DOI: 10.1046/j.1365-8711.2000.03071.x; Website of FFTLog: casa.colorado.edu/~ajsh/FFTLog. |
| [Talman_1978] | Talman, J. D., 1978, Numerical Fourier and Bessel transforms in logarithmic variables: Journal of Computational Physics, 29, pages 35-48; DOI: 10.1016/0021-9991(78)90107-9. |
Released to the public domain under the CC0 1.0 License. Be kind and give credits to [Hamilton_2000].