HE Gaiyun and SONG Zhanjie, “An Almost Sure Result on Sampling of Bandlimited Random Signals,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 747-750, 2013,
Citation: HE Gaiyun and SONG Zhanjie, “An Almost Sure Result on Sampling of Bandlimited Random Signals,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 747-750, 2013,

An Almost Sure Result on Sampling of Bandlimited Random Signals

Funds:  This work is partially supported by the National Natural Science Foundation of China (No.60872161;No.60932007).
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  • Corresponding author: HE Gaiyun, SONG Zhanjie
  • Received Date: 2011-05-01
  • Rev Recd Date: 2012-05-01
  • Publish Date: 2013-09-25
  • The Shannon-Nyquist sampling theorem for deterministic signals is a fundamental result in the field of telecommunication and signal processing, and many results on this topic have been obtained. However, very few results on random signals have been published, after Kolmogorov mentioned the importance of Shannon-formula for stochastic signals in 1956. In this paper, following the almost sure result for bandlimited stochastic processes proposed by Seip in 1990, we give an almost sure result of the classical sampling theorem for bandlimited random signals with local average sampling.
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  • C.E. Shannon, “Communication in the presence of noise”, Proceedings of the IRE, Vol.37, No.1, pp.10-21, 1949.
    W. Chen, “A fast convergence algorithm for band-limited extrapolationb y sampling”, IEEE Trans. Signal Processing,Vol.57, No.1, pp.161-167, 2009.
    Y. Yang, J. Deng, W. Tang, C. Wu, “Nonuniform extrema resampling and empirical mode decomposition”, Chinese Journal of Electronics, Vol.18, No.4, pp.759-762, 2009.
    F. Marvasti, Nonuniform Sampling: Theory and Practice,Newyork: Kluwer Academic/Plenum Publisher, 2001.
    M. Unser, “Sampling—50 years after Shannon”, Proceedings oft he IEEE, Vol.88, No.4, pp.569-587, 2000.
    W. Sun and X. Zhou, “Reconstruction of band-limited signalsf rom local averages”, IEEE Trans. Inform. Theory, Vol.48,N o.11, pp.2955-2963, 2002.
    Z. Song, S. Yang and X. Zhou, “Approximation of signals froml ocal averages”, Applied Mathematics Letters, Vol.19, No.12,p p.1414-1420, 2006.
    A.N. Kolmogorov, On the Shannon theory of transmission in thec ase of continuous signals, TRE Trans Inform Theory, Vol.2,N o.4, pp.102-108, 1956.
    Z. Song, W. Sun, S. Yang and G. Zhu, “Approximation of weaks ense stationary stochastic processes from local averages”, Sciencein China Series A—Mathematics, Vol.50, No.4, pp.457-463, 2007.
    Z. Song, W. Sun, X. Zhou and Z. Hou, “An average samplingt heorem for bandlimited stochastic processes”, IEEE Trans. Inform.T heory, Vol.53, No.12, pp.4798-4800, 2007.
    K. Seip, “A note on sampling of bandlimited stochastic processes”,I EEE Trans. Inform. Theory, Vol.36, No.5, pp.1186,1 990.
    G. He, Z. Song, “Approximation of WKS sampling theorem onr andom signals”, Numerical Functional Analysis and Optimization,Vol.32, No.4, pp.397-408, 2011.
    H. Boche, U.J. Monich, “Approximation of wide-sense stationarys tochastic processes by Shannon sampling series”, IEEET rans. Inform. Theory, Vol.56, No.12, pp.6459-6469, 2010.
    A. Napolitano, “Sampling of spectrally correlated processes”,I EEE Trans. Signal Processing, Vol.59, No.2, pp.525-539, 2011.
    R.M. Young, An Introduction to Nonharmonic Fourier Series,New York/Academic Press, 1980.
    Z. Li and R. Wu, A Course of Studies on Stochastic Processes,B eijing/ High Education Press, 1987. (in chinese)
    P.L. Butzer, “The Hausdorff-Young theorems of Fourier analysis and their impact”, J Fourier Anal. Appl., Vol.1, No.2,p p.113-130, 1994.
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