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An Asymptotic Sampling Recomposition Theorem for Gaussian Signals |
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| Authors: | Almudena Antu?a Juan L G Guirao Miguel A L??pez |
| Institution: | 1. Departamento de An??lisis Econ??mico y Finanzas, Universidad de Castilla-La Mancha Facultad de CC. Sociales, 16071, Cuenca, (Castilla-La Mancha), Spain 2. Departamento de Matem??tica Aplicada y Estad??stica, Universidad Polit??cnica de Cartagena, Campus de la Muralla, 30203, Cartagena, (Regi??n de Murcia), Spain 3. Departamento de Matem??ticas, Universidad de Castilla-La Mancha E.U. Polit??cnica de Cuenca, 16071, Cuenca, (Castilla-La Mancha), Spain |
| 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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