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Multichannel Sampling of Signals Band-Limited in Offset Linear Canonical Transform Domains

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Abstract

The aim of the multichannel sampling is the reconstruction of a band-limited signal f(t), from the samples of the responses of M linear time invariant systems, each sampled by the 1/Mth Nyquist rate. As the offset linear canonical transform (OLCT) has been found wide applications in signal processing and optics fields, it is necessary to consider the multichannel sampling based on offset linear canonical transform. In this paper, we develop a multichannel sampling theorem for signals band-limited in offset linear canonical transform domains. Moreover, by designing different OLCT filters, reconstruction formulas for uniform sampling from the signal, from the signal and its first derivative or its generalized Hilbert transform are obtained based on the derived multichannel sampling theorem. Since recurrent nonuniform sampling for the signal has valuable applications, reconstruction expression for recurrent nonuniform samples of the signal band-limited in the offset linear canonical transform domain is also obtained by using the derived multichannel sampling theorem and the properties of the offset linear canonical transform.

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Acknowledgements

This work was supported in part by the Fundamental Research Funds for the Central Universities, Southwest University for Nationalities (No. 11NZYQN18), the National Natural Science Foundation of China (No. 60672029), and also supported by the Fundamental Research Funds of Southwest University for Nationalities (No. 12NZYTH01).

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Xiang, Q., Qin, KY. & Huang, QZ. Multichannel Sampling of Signals Band-Limited in Offset Linear Canonical Transform Domains. Circuits Syst Signal Process 32, 2385–2406 (2013). https://doi.org/10.1007/s00034-013-9575-6

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  • DOI: https://doi.org/10.1007/s00034-013-9575-6

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