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Computing Recomposition of Maps with a New Sampling Asymptotic Formula
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Open Journal of Discrete Mathematics·Volume 01 (2011)·Pages 43–49·Published 5 July 2011·DOI10.4236/ojdm.2011.12006
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Abstract
The aim of the present paper is to state an asymptotic property Ρ of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band- limited signal. It generalizes in the limit the results stated by Marvasti et al. [7] and Agud et al. [1]. We show that Ρ is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e<sup>-Λt<sup>2</sup> </sup> ,Λ∈R<sup>+</sup>, hold Ρ. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e<sup>-Λt<sup>2</sup> </sup> .
KeywordsBand-Limited SignalShannon's Sampling TheoremApproximation Theory
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