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Stochastic Formulation of (a,b,c,d)-Bandlimited Signal Reconstruction

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Abstract

Many reconstruction algorithms for bandlimited signals associated with linear canonical transform have been proposed. However, these reconstruction algorithms have assumed a deterministic signal with no noise. This assumption is almost never satisfied in real applications. Deterministic formulations do not accurately describe the random nature of the reconstruction problem when the signal is best considered as a random process, possibly corrupted by noise. In this paper, we formulate the reconstruction problem of bandlimited signal associated with linear canonical transform within a stochastic framework. A stochastic, minimum mean squared error reconstruction algorithm from noisy observations is proposed, from which four commonly used reconstruction algorithms for different stochastic models are derived. By the derived algorithms, the relationship between the theories for the stochastic and deterministic cases is clarified. The relationship between the theories for the noise-free and noisy cases is also clarified.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grants 61102151 and 51105392), the Natural Science Foundation Project of Chongqing (Grants cstc2012jjA40048 and cstc2011jjA70006), and by the Fundamental Research Funds for the Central Universities (Grant CDJRC10110005)

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Correspondence to Daiping Song.

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Song, D., Zhao, H. Stochastic Formulation of (a,b,c,d)-Bandlimited Signal Reconstruction. Circuits Syst Signal Process 34, 2053–2064 (2015). https://doi.org/10.1007/s00034-014-9932-0

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  • DOI: https://doi.org/10.1007/s00034-014-9932-0

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