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Descripción
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| In order to avoid most of the problems associated with classical Shannon?s sampling theory, nowadays signals are assumed to belong to some shift-invariant subspace. In this work we consider a general shift-invariant space V of L2 with a set of r stable generators. Besides, in many common situations the available data of a signal are samples of some filtered versions of the signal itself taken at a sub-lattice of Z^d. This leads to the problem of generalized sampling in shift-invariant spaces. Assuming that the L2-norm of the generalized samples of any function f of V are stable with respect to the L2-norm of the signal f, we derive frame expansions in the shift-invariant subspace allowing the recovery of the signals in V from the available data. The mathematical technique used here mimics the Fourier duality technique which works for classical Paley-Wiener spaces. | |
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Internacional
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Si |
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DOI
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10.1007/978-1-4614-4145-8 |
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Edición del Libro
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1 |
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Editorial del Libro
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Springer |
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ISBN
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978-1-4614-4145-8 |
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Serie
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Lecture notes in Electrical Engineering |
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Título del Libro
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Multiscale Signal Analysis and Modeling |
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Desde página
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51 |
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Hasta página
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81 |