On Multiangle Discrete Fractional Periodic Transforms

TL;DR

This paper generalizes the multiangle centered discrete fractional Fourier transform to a broader class of M-periodic transforms, reducing computational complexity for efficient time-frequency analysis.

Contribution

It introduces a unified framework for M-periodic transforms including Fourier, sine, cosine, Hadamard, and Hartley, and reduces FFT computations by exploiting symmetries.

Findings

Generalized MA-CDFRFT to M-periodic transforms.

Halved the number of FFTs needed for computation.

Enabled more resource-efficient time-frequency analysis.

Abstract

The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among others, include the standard discrete Fourier, discrete sine, discrete cosine, Hadamard and discrete Hartley transform. Furthermore, we exploit the symmetries inherent to the MA-CDFRFT and our novel multiangle standard discrete fractional Fourier transform (MA-DFRFT) to halve the number of FFTs needed to compute these transforms, which paves the way for applications in resource-constrained environments.