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Recovery of Bandlimited Signals in Linear Canonical Transform Domain from Noisy Samples

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Abstract

The linear canonical transform (LCT) has been shown to be a useful and powerful tool for signal processing and optics. Many reconstruction strategies for bandlimited signals in LCT domain have been proposed. However, these reconstruction strategies can work well only if there are no errors associated with the numerical implementation of samples. Unfortunately, this requirement is almost never satisfied in the real world. To the best of the author’s knowledge, the statistical problem of LCTed bandlimited signal recovery in the presence of random noise still remains unresolved. In this paper, the problem of recovery of bandlimited signals in LCT domain from discrete and noisy samples is studied. First, it is shown that the generalized Shannon-type reconstruction scheme for bandlimited signals in LCT domain cannot be directly applied in the presence of noise since it leads to an infinite mean integrated square error. Then an orthogonal and complete set for the class of bandlimited signals in LCT domain is proposed; and further, an oversampled version of the generalized Shannon-type sampling theorem is derived. Based on the oversampling theorem and without adding too much complexity, a reconstruction algorithm for bandlimited signals in LCT domain from discrete and noisy observations is set up. Moreover, the convergence of the proposed reconstruction scheme is also proved. Finally, numerical results and potential applications of the proposed reconstruction algorithm are given.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grants 61102151, 51105392, and 61271261), the Natural Science Foundation Project of Chong Qing (Grants cstc2012jjA40048, cstc2011jjA70006, and cstc2011BA2041), the Natural Science Foundation of CQUPT (Grant A2012-83), and by the Fundamental Research Funds for the Central Universities (Grants CDJZR 10110002 and CDJRC10110005).

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Authors and Affiliations

  1. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Hui Zhao & Ruyan Wang

  2. College of Mechanical Engineering, Chongqing University, Chongqing, 400044, China

    Daiping Song

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  1. Hui Zhao
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  2. Ruyan Wang
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  3. Daiping Song
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Correspondence to Hui Zhao.

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Zhao, H., Wang, R. & Song, D. Recovery of Bandlimited Signals in Linear Canonical Transform Domain from Noisy Samples. Circuits Syst Signal Process 33, 1997–2008 (2014). https://doi.org/10.1007/s00034-013-9723-z

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  • DOI: https://doi.org/10.1007/s00034-013-9723-z

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