A sampling theorem for the fractional Fourier transform without band-limiting constraints

Shi, Jun and Xiang, Wei and Liu, Xiaoping and Zhang, Naitong (2014) A sampling theorem for the fractional Fourier transform without band-limiting constraints. Signal Processing, 98. pp. 158-165. ISSN 0165-1684

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Abstract

The fractional Fourier transform (FRFT), a generalization of the Fourier transform, has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of the FRFT consider the class of band-limited signals. However, in the real world, many analog signals encountered in practical engineering applications are non-bandlimited. The purpose of this paper is to propose a sampling theorem for the FRFT, which can provide a suitable and realistic model of sampling and reconstruction for real applications. First, we construct a class of function spaces and derive basic properties of their basis functions. Then, we establish a sampling theorem without band-limiting constraints for the FRFT in the function spaces. The truncation error of sampling is also analyzed. The validity of the theoretical derivations is demonstrated via simulations.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2013 Elsevier B.V. Permanent restricted access to Published version due to publisher copyright policy.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 19 Jan 2014 06:11
Last Modified: 01 Jul 2016 04:15
Uncontrolled Keywords: Fourier transform; function spaces; Riesz bases; sampling theorem; truncation error
Fields of Research : 10 Technology > 1005 Communications Technologies > 100507 Optical Networks and Systems
09 Engineering > 0906 Electrical and Electronic Engineering > 090609 Signal Processing
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
Socio-Economic Objective: B Economic Development > 89 Information and Communication Services > 8901 Communication Networks and Services > 890199 Communication Networks and Services not elsewhere classified
Identification Number or DOI: 10.1016/j.sigpro.2013.11.026
URI: http://eprints.usq.edu.au/id/eprint/24561

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