Author(s)

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

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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 .

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

A. Antuña, J. Guirao and M. López, "Computing Recomposition of Maps with a New Sampling Asymptotic Formula," Open Journal of Discrete Mathematics, Vol. 1 No. 2, 2011, pp. 43-49. doi: 10.4236/ojdm.2011.12006.