ISSN:
1531-5851
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Functions belonging to various Paley-Wiener spaces have representations in sampling series. When a function does not belong to such a space, the sampling series may converge, not to the object function but to an "alias" of it, and an aliasing error is said to occur. Aliasing error bounds are derived for one- and two-channel sampling series analogous to the Whittaker-Kotel’nikov-Shannon series, and for the multi-band sampling series, and a "derivative" extension of it, due to Dodson, Beaty, et al. The Poisson summation formula is a basic tool throughout. Aliasing in the one-channel case is shown to arise from a transformation with similarities to a projection. Where possible, the sharpness of the error bounds is discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s00041-001-4003-x
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