Sampling theorems in function spaces for frames associated with linear canonical transform

The linear canonical transform (LCT) has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of this transform were derived from the LCT band-limited signal viewpoint. However, in the real world, many analog signals encountered in practical engineering appli...

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Bibliographic Details
Published in:Signal processing 2014-05, Vol.98, p.88-95
Main Authors: Shi, Jun, Liu, Xiaoping, Zhang, Qinyu, Zhang, Naitong
Format: Article
Language:English
Subjects:
Applied sciences
Band theory
Derivation
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Frames
Function space
Function spaces
Information, signal and communications theory
Linear canonical transform
Riesz bases
Sampling
Sampling theorem
Sampling, quantization
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Theorems
Transforms
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Summary:The linear canonical transform (LCT) has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of this transform were derived from the LCT band-limited signal viewpoint. However, in the real world, many analog signals encountered in practical engineering applications are non-bandlimited. The purpose of this paper is to derive sampling theorems of the LCT in function spaces for frames without band-limiting constraints. We extend the notion of shift-invariant spaces to the LCT domain and then derive a sampling theorem of the LCT for regular sampling in function spaces with frames. Further, the theorem is modified to the shift sampling in function spaces by using the Zak transform. Sampling and reconstructing signals associated with the LCT are also discussed in the case of Riesz bases. Moreover, some examples and applications of the derived theory are presented. The validity of the theoretical derivations is demonstrated via simulations. •Some properties of the function spaces associated with the LCT are presented.•A sampling theorem for the LCT in function spaces with frames is established.•A shift-sampling theorem for the LCT in function spaces is derived.•Some new results of sampling in the LCT domain are derived for Riesz bases.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2013.11.013