Perfect reconstruction formulas and bounds on aliasing error in sub-Nyquist nonuniform sampling of multiband signals

Raman Venkataramani, Yoram Bresler

Research output: Contribution to journalArticlepeer-review

Abstract

We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class B(F) of multiband signals with spectral support F, at rates arbitrarily close to the Landau minimum rate equal to the Lebesgue measure of F, even when F does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the `span of F' (the smallest interval containing F) which is a bigger class than the valid signals B(F), band-limited to F. We also examine the performance of the reconstruction system when the input contains additive sample noise.

Original languageEnglish (US)
Pages (from-to)2173-2183
Number of pages11
JournalIEEE Transactions on Information Theory
Volume46
Issue number6
DOIs
StatePublished - Sep 2000

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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