Abstract
For any Gaussian signal and every given sampling frequency we prove an asymptotic property of type Shannon’s sampling theorem, based on normalized cardinal sines, which keeps constant the sampling frequency. We generalize the Shannon’s sampling theorem for a class of non band–limited signals which plays a central role in the signal theory, the Gaussian map is the unique function which reachs the minimum of the product of the temporal and frecuential width. This solve a conjecture stated in [1] and suggested by [3].
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This work has been partially supported by MCI (Ministerio de Ciencia e Innovación) and FEDER (Fondo Europeo Desarrollo Regional), grant number MTM2008–03679/MTM, Fundación Séneca de la Región de Murcia, grant number 08667/PI/08 and JCCM (Junta de Comunidades de Castilla-La Mancha), grant number PEII09-0220-0222.
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Antuña, A., Guirao, J.L.G. & López, M.A. An Asymptotic Sampling Recomposition Theorem for Gaussian Signals. Mediterr. J. Math. 8, 349–367 (2011). https://doi.org/10.1007/s00009-010-0076-6
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DOI: https://doi.org/10.1007/s00009-010-0076-6