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

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

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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.

Item ID: 43308
Item Type: Article (Research - C1)
ISSN: 1872-7557
Keywords: fractional Fourier transform, function spaces, Riesz bases, sampling theorem, truncation error
Funders: National Basic Research Program of China (NBRP), National Science Foundation of China (NSFC)
Projects and Grants: NBRP 2013CB329003, NSFC 61171110
Date Deposited: 24 Feb 2016 07:47
FoR Codes: 09 ENGINEERING > 0906 Electrical and Electronic Engineering > 090609 Signal Processing @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 100%
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