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Published November 2013 | public
Book Section - Chapter

Reflections on Sampling-Filters for Compressive Sensing and Finite-Innovations-Rate Models

Abstract

This paper revisits sampling-filters for signals having a finite rate of innovations. Such filters arise in many applications including digital communications and compressive sensing, and mulitchannel versions of these systems have been considered in the past. The main focus of this paper is on sampling-filters that result in perfect reconstruction (PR), or zero-forcing (ZF). Conditions for existence of these filters are expressed both in terms of bandwidth requirement and in the framework of Riesz basis. Many practical advantages induced by the Riesz basis property are also pointed out. When the sampling filters for PR exist, they are in general not unique. Optimum filters that minimize the effect of noise are discussed and compared with energy compaction filters, which are suboptimal.

Additional Information

© 2013 IEEE. This work was supported in parts by the ONR grant N00014-11-1-0676, and the California Institute of Technology.

Additional details

Created:
August 19, 2023
Modified:
January 13, 2024