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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Text (Accepted Version)
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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/School / Institute/Centre: | Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering (1 Jul 2013 -) |
| Faculty/School / Institute/Centre: | Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering (1 Jul 2013 -) |
| 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 (2008): | 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 |
| Fields of Research (2020): | 40 ENGINEERING > 4006 Communications engineering > 400605 Optical fibre communication systems and technologies 40 ENGINEERING > 4006 Communications engineering > 400607 Signal processing 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490406 Lie groups, harmonic and Fourier analysis |
| Socio-Economic Objectives (2008): | 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: | https://doi.org/10.1016/j.sigpro.2013.11.026 |
| URI: | http://eprints.usq.edu.au/id/eprint/24561 |
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