Sampling signals from a union of shift-invariant subspaces

Yue M. Lu, Minh N Do

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study a sampling problem where sampled signals come from a known union of shift-invariant subspaces and the sampling operator is a linear projection of the sampled signals into a fixed shift-invariant subspace. In practice, the sampling operator can be easily implemented by a multichannel uniform sampling procedure. We present necessary and sufficient conditions for invertible and stable sampling operators in this framework, and provide the corresponding minimum sampling rate. As an application of the proposed general sampling framework, we study the specific problem of spectrum-blind sampling of multiband signals. We extend the previous results of Bresler et al. by showing that a large class of sampling kernels can be used in this sampling problem, all of which lead to stable sampling at the minimum sampling rate.

Original languageEnglish (US)
Title of host publicationWavelets XII
DOIs
StatePublished - Dec 1 2007
EventWavelets XII - San Diego, CA, United States
Duration: Aug 26 2007Aug 29 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume6701
ISSN (Print)0277-786X

Other

OtherWavelets XII
CountryUnited States
CitySan Diego, CA
Period8/26/078/29/07

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Keywords

  • Projection
  • Sampling
  • Shift-invariant subspaces
  • Union of subspaces

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Lu, Y. M., & Do, M. N. (2007). Sampling signals from a union of shift-invariant subspaces. In Wavelets XII [670122] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 6701). https://doi.org/10.1117/12.733331