Sampling expansion for irregularly sampled signals in fractional Fourier transform domain

Liu, Xiaoping and Shi, Jun and Xiang, Wei and Zhang, Qinyu and Zhang, Naitong (2014) Sampling expansion for irregularly sampled signals in fractional Fourier transform domain. Digital Signal Processing, 34. pp. 74-81. ISSN 1051-2004


Real-world signals are often not band-limited, and in many cases of practical interest sampling points are not always measured regularly. The purpose of this paper is to propose an irregular sampling theorem for the fractional Fourier transform (FRFT), which places no restrictions on the input signal. First, we construct frames for function spaces associated with the FRFT. Then, we introduce a unified framework for sampling and reconstruction in the function spaces. Based upon the proposed framework, an FRFT-based irregular sampling theorem without band-limiting constraints is established. The theoretical derivations are validated via numerical results.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2014 Elsevier Inc. 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
Date Deposited: 10 Feb 2015 06:23
Last Modified: 14 Apr 2015 06:49
Uncontrolled Keywords: Fourier transform; fractional; function spaces; irregular sampling; non-bandlimited; sampling theorem
Fields of Research : 09 Engineering > 0906 Electrical and Electronic Engineering > 090609 Signal Processing
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
01 Mathematical Sciences > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.dsp.2014.08.004

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