Fractional Fourier Transforms

Implementation of the Fast Fractional Fourier Transform based on Javier García, David Mas, and Rainer G. Dorsch, "Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm," Appl. Opt. 35, 7013-7018 (1996)

frfft(arr, p; shift=false, method=:garcia)

Calculates the fractional Fast Fourier transform (FRFFT) of the order p of arr. No dims argument is supported yet.

If shift=false the FRFFT is calculated around the first entry. If shift=true the FRFFT is calculated aroound the center.


Several implementation exists. The following are implemented:

  • method=:garcia: A convolutional approach based on 2 FFTs. See García, J., Mas, D., & Dorsch, R. G. (1996). Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm. Applied Optics, 35(35), 7013. doi:10.1364/ao.35.007013