Moving average restoration of bandlimited signals from noisy observations

The purpose of this paper is to describe the extension of the Whittaker-Shannon sampling theorem to reconstruction of bandlimited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon sampling scheme is not consistent in the case of noisy measur...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1997-12, Vol.45 (12), p.2967-2976
Main Authors: Krzyzak, A., Rafajlowicz, E., Pawlak, M.
Format: Article
Language:English
Subjects:
Applied sciences
Computer simulation
Convergence
Councils
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Information, signal and communications theory
Interpolation
Reconstruction algorithms
Sampling methods
Sampling, quantization
Signal and communications theory
Signal processing algorithms
Signal restoration
Signal sampling
Signal, noise
Smoothing methods
Telecommunications and information theory
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Summary:The purpose of this paper is to describe the extension of the Whittaker-Shannon sampling theorem to reconstruction of bandlimited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon sampling scheme is not consistent in the case of noisy measurements, and new reconstruction algorithms based on the moving average smoothing are proposed. The weak and strong consistency of the algorithms is established, and the rate of convergence is investigated. The theory is verified in the computer simulations.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.650257