Uncertainty Principles for the Offset Linear Canonical Transform

Uncertainty Principles for the Offset Linear Canonical Transform Circuits Syst Signal Process https://doi.org/10.1007/s00034-018-0863-z Uncertainty Principles for the Offset Linear Canonical Transform Haiye Huo Received: 26 October 2017 / Revised: 24 May 2018 / Accepted: 25 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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. Keywords Offset linear canonical transform · Uncertainty principle · Logarithmic uncertainty estimate · Entropic inequality · Localization 1 Introduction Uncertainty principle (UP) plays an important role in quantum mechanics [9] and signal processing [2]. In quantum mechanics, UP was first proposed by the German physicist W. Heisenberg in 1927 [9]. It basically says that the more precisely the position of a particle is determined, the less precisely its momentum http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Circuits, Systems and Signal Processing Springer Journals

Uncertainty Principles for the Offset Linear Canonical Transform

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Engineering; Circuits and Systems; Electrical Engineering; Signal,Image and Speech Processing; Electronics and Microelectronics, Instrumentation
ISSN
0278-081X
eISSN
1531-5878
D.O.I.
10.1007/s00034-018-0863-z
Publisher site
See Article on Publisher Site

Abstract

Circuits Syst Signal Process https://doi.org/10.1007/s00034-018-0863-z Uncertainty Principles for the Offset Linear Canonical Transform Haiye Huo Received: 26 October 2017 / Revised: 24 May 2018 / Accepted: 25 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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. Keywords Offset linear canonical transform · Uncertainty principle · Logarithmic uncertainty estimate · Entropic inequality · Localization 1 Introduction Uncertainty principle (UP) plays an important role in quantum mechanics [9] and signal processing [2]. In quantum mechanics, UP was first proposed by the German physicist W. Heisenberg in 1927 [9]. It basically says that the more precisely the position of a particle is determined, the less precisely its momentum

Journal

Circuits, Systems and Signal ProcessingSpringer Journals

Published: Jun 4, 2018

References

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