Sampling theory in abstract reproducing kernel Hilbert space

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Let H be a separable Hilbert space and k(t) an H-valued function on a subset Ω of the real line R such that {k(t) t ε Ω} is total in H. Then {fx:= (x, k(t))H x ε H} becomes a reproducing kernel Hilbert space (RKHS) in a natural way. Here, we develop a sampling formula for functions in this RKHS, which generalizes the well-known celebrated Whittaker-Shannon-Kotelnikov sampling formula in the Paley-Wiener space of band-limited signals. To be more precise, we develop a multi-channel sampling formula in which each channel is given a rather arbitrary sampling rate. We also discuss stability and oversampling. ? 2007 Sampling Publishing.
Publisher
Sampling Publishing
Issue Date
2007-01
Language
English
Citation

SAMPLING THEORY IN SIGNAL AND IMAGE PROCESSING, v.6, no.1, pp.109 - 121

ISSN
1530-6429
URI
http://hdl.handle.net/10203/24706
Appears in Collection
MA-Journal Papers(저널논문)
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