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Discrete Time-Frequency Analysis and Sampling

  • Gerald Kaiser
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Summary

The reconstruction formula for windowed Fourier transforms is highly redundant since it uses all the notes gω,t to recover the signal and these notes are linearly dependent. In this chapter we prove a reconstruction formula using only a discrete subset of notes. Although still redundant, this reconstruction is much more efficient and can be approximated numerically by ignoring notes with very large time or frequency parameters. The present reconstruction is a generalization of the well-known Shannon sampling theorem, which underlies digital recording technology. We discuss its advantages over the latter, including the possibility of cutting the frequency spectrum of a signal into a number of "subbands" and processing these subbands in parallel.

Keywords

Compact Support Sampling Theorem Frame Bound Gaussian Window Reconstruction Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2011

Authors and Affiliations

  1. 1.Center for Signals and WavesAustinUSA

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