A sampling theorem for the fractional Fourier transform without band-limiting constraints
Article
Article Title | A sampling theorem for the fractional Fourier transform without band-limiting constraints |
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ERA Journal ID | 4509 |
Article Category | Article |
Authors | Shi, Jun (Author), Xiang, Wei (Author), Liu, Xiaoping (Author) and Zhang, Naitong (Author) |
Journal Title | Signal Processing |
Journal Citation | 98, pp. 158-165 |
Number of Pages | 8 |
Year | 2014 |
Place of Publication | Netherlands |
ISSN | 0165-1684 |
1872-7557 | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.sigpro.2013.11.026 |
Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0165168413004623 |
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. |
Keywords | Fourier transform; function spaces; Riesz bases; sampling theorem; truncation error |
ANZSRC Field of Research 2020 | 400605. Optical fibre communication systems and technologies |
400607. Signal processing | |
490406. Lie groups, harmonic and Fourier analysis | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Harbin Institute of Technology, China |
School of Mechanical and Electrical Engineering | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q2377/a-sampling-theorem-for-the-fractional-fourier-transform-without-band-limiting-constraints
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