A sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain

TL;DR

This paper establishes a new sampling theorem for shift-invariant spaces related to the fractional Fourier transform, broadening classical and prior sampling results in signal processing.

Contribution

It introduces a generalized sampling theorem for shift-invariant spaces in the fractional Fourier transform domain, extending classical and existing theorems.

Findings

Provides a unified framework for sampling in fractional Fourier domains

Extends classical Whittaker-Shannon-Kotelnikov sampling theorem

Enhances understanding of shift-invariant spaces in signal processing

Abstract

As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain. The resulting sampling theorem extends not only the classical Whittaker-Shannon-Kotelnikov sampling theorem associated with the fractional Fourier transform domain, but also extends the prior sampling theorems on shift-invariant spaces.