On the Sampling Theorem in Hilbert Spaces

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Abstract

Although the sampling theorem is well known, its demon- stration assumes generalized delta functions and periodic signals, which are not defined in Hilbert spaces, as well as bandlimited signals which not exist in reality because they must have infinite duration. In this paper, we consider the sampling theorem in Hilbert spaces. We present a simple and complete demonstration of the sampling theorem that uses only signals defined in Hilbert spaces, i.e., we do not use generalized delta func- tions or periodic signals. We also establish the aliasing ef- fects as a corollary of the theorem.
Original languageUnknown
Title of host publicationProceedings of the 10th IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA 2013)
Pages161-164
DOIs
Publication statusPublished - 1 Jan 2013
EventSPPRA 2013: 10th IASTED International Conference on Signal Processing, Pattern Recognition and Applications -
Duration: 1 Jan 2013 → …

Conference

ConferenceSPPRA 2013: 10th IASTED International Conference on Signal Processing, Pattern Recognition and Applications
Period1/01/13 → …

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