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TitleGroebner basis methods for multichannel sampling with unknown offsets
Author(s) Luciano Sbaiz, Patrick Vandewalle, Martin Vetterli
TypeArticle in Journal
AbstractIn multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear in the signal parameters. We show that when the basis functions for the signal space are related to polynomials, we can express the joint offset and signal parameter estimation as a set of polynomial equations. This is the case for example with polynomial signals or Fourier series. The unknown offsets and signal parameters can be computed exactly from such a set of polynomials using Gröbner bases and Buchberger
KeywordsAliasing, Sampling, Multichannel sampling, Offset estimation, Groebner basis
URL http://www.sciencedirect.com/science/article/pii/S1063520307001303
JournalApplied and Computational Harmonic Analysis
Pages277 - 294
Translation No
Refereed No