Fast Fractional Fourier Transform

This is an implementation of the one dimensional discrete fractional fourier transform (DFrFT) in rust.

Previews

A visual preview of results of the discrete fractional fourier transform can be seen here.

References

The implementation is manually translated from the the Matlab code provided by A.Bultheel, H. Martínez-Sulbaran. in their paper Computation of the Fractional Fourier Transform.

They provided two different Matlab implementations frft.m and frft.m.

Both have been translated to rust as frfft1d::strategy::Basic and frfft1d::strategy::Fast respectively.

Usage

use frfft1d::strategy::FastFrft;

use frfft1d::strategy::BasicFrft;

// The Signal to be transformed.
let mut signal = [
    Complex::new(1.0, 0.0),
    Complex::new(0.0, 0.0),
    Complex::new(0.0, 0.0),
    Complex::new(0.0, 0.0),
];

// prepare the calculation for the given signal length.
let mut frft = FastFrft::new(signal.len());

// transform the signal inplace
// the seconds parameter is the fractional exponent of the transform.
// 1.0 corresponds to the classic DFT/FFT.
frft.process_scaled(&mut signal, 1.0);
// 2.0 corresponds to applying the DFT/FFT twice.
frft.process_scaled(&mut signal, 2.0);
// 3.0 corresponds to applying the DFT/FFT three times, which is inturn the same as applying the inverse DFT (iDFT)
frft.process_scaled(&mut signal, 3.0);
// 4.0 corresponds to applying the DFT/FFT four times, which does not change the signal at all.
frft.process_scaled(&mut signal, 4.0);

// The fractional fourier transform does also allow non integer exponents.
// 0.5 corresponds to applying the the DFT only "half".
frft.process_scaled(&mut signal, 0.5);