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Approximation of signals using measured sampled values and error analysis. (English) Zbl 1089.94503

Summary: If a signal \(f\) is bandlimited to \([-\pi w,\pi w]\) for some \(w>0\), according to the Shannon sampling, it can be fully reconstructed from its sampled values \(f(k/w)\), \(k\in\mathbf Z\). Here a sampled value is viewed as a linear functional acting on the underlying signal. Such a particular measured sampled value is an integral average of \(f\) around \(k/w\). The first aim of this paper is to present a systematic approach to error analysis for sampling series with measured sampled values, including amplitude and jitter errors, that will also cover the classical instances. The second aim is to study the corresponding situation in the multivariate case when the sinc kernel is replaced by a general kernel (having faster decay). Special emphasis is placed upon constants involved in the error estimates.

MSC:

94A20 Sampling theory in information and communication theory
41A25 Rate of convergence, degree of approximation
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