Computing Recomposition of Maps with a New Sampling Asymptotic Formula

Almudena Antuña, Juan L. G. Guirao, Miguel A. López

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DOI: 10.4236/ojdm.2011.12006                

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^-Λt2 ,Λ∈R⁺, hold Ρ. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e^-Λt2 .

Keywords

Band-Limited Signal, Shannon's Sampling Theorem, Approximation Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

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