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
Abstract
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 (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: | 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 (2008): | 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 Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | https://doi.org/10.1016/j.dsp.2014.08.004 |
| URI: | http://eprints.usq.edu.au/id/eprint/26723 |
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