Uncertainty Principles for the Offset Linear Canonical Transform

TL;DR

This paper extends various classical uncertainty principles to the offset linear canonical transform (OLCT), a general framework encompassing several important transforms in signal processing and optics.

Contribution

It introduces the first comprehensive extension of multiple uncertainty principles to the OLCT domain, broadening theoretical understanding.

Findings

Extended Nazarov's UP to OLCT

Extended Hardy’s UP to OLCT

Extended Beurling’s UP to OLCT

Abstract

The offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical transform. In this paper, to characterize simultaneous localization of a signal and its OLCT, we extend some different uncertainty principles (UPs), including Nazarov's UP, Hardy's UP, Beurling's UP, logarithmic UP and entropic UP, which have already been well studied in the Fourier transform domain over the last few decades, to the OLCT domain in a broader sense.