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Title: Postfiltering versus prefiltering for signal recovery from noisy samples
Authors: Pawlak, M
Rafajlowicz, E
Krzyzak, A
Keywords: band-limited signals
non-band-limited signals
rate of convergence
signal recovery
strong convergence
Whittaker-Shannon (WS) sampling theorem
Issue Date: 31-Dec-2003
Citation: 0018-9448; IEEE TRANS INFORM THEORY, DEC 2003, vol. 49, no. 12, p.3195 to 3212.
Abstract: We consider the extension of the Whittaker-Shannon (WS) reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited. Observing that in this situation the classical sampling expansion yields inconsistent reconstruction, we introduce a class of signal recovery methods with a smooth correction of the interpolation series. Two alternative data smoothing methods are examined based either on a global postfiltering or a local data presmoothing. We assess the accuracy of the methods by the global L-2 error. Both band-limited and non-band-limited signals are considered. A general class of correlated noise processes is taken into account. The weak and strong rates of convergence of the algorithms are established and their relative efficiency is discussed. The influence of noise memory and its moment structure on the accuracy is thoroughly examined.
Appears in Collection(s):Research Publications (UofM Student, Faculty and Staff only access)

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