# 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)

`FourierTools.frfft`

— Function`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.

**Methods**

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