SciFracX / FractionalTransforms.jl

FractionalTransforms.jl: A Julia package aiming at providing fractional order transforms with high performance.

FractionalTransforms.jl

Installation

If you have already installed Julia, you can install FractionalTransforms.jl in REPL using Julia package manager:

pkg> add FractionalTransforms

Quick start

Fractional Fourier Transform

Compute the Fractional Fourier transform by the following command:

frft(signal, order)

Fractional Sine Transform

Compute the Fractional Sine transform by the following command:

julia> frst(signal, order, p)

Fractional Cosine Transform

Compute the Fractional Cosine transform by the following command:

julia> frct(signal, order, p)

Introduce

The custom Fourier Transform transforms the input signal from time domain to frequency domain, the Fractional Fourier transform, in a more generalized aspect, can transform the input signal to the fractional domain, reveal more properties and features of the signal.

Plans

• Add more examples relating to signal processing, image processing etc.
• Cover more algorithms, including Fractional Hadamard Transform, Fractional Gabor Transform...

Acknowledgements

I would like to express gratitude to

• Jeffrey C. O'Neill for what he has done in DiscreteTFDs.
• Digital computation of the fractional Fourier transform by H.M. Ozaktas; O. Arikan; M.A. Kutay; G. Bozdagt
• The discrete fractional cosine and sine transforms by Pei, Soo-Chang and Yeh, Min-Hung.
• https://nalag.cs.kuleuven.be/research/software/FRFT/

Please note that FRFT, FRST and FRCT are adapted from Matlab files, credits go to the original authors, bugs are my own.