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Discrete Time-Scale Analysis

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

Summary

In Chapter 3, we expressed a signal / as a continuous superposition of a family of wavelets Ψs,t, with the CWT ƒ (s,t) as the coefficient function. In this chapter we discuss discrete constructions of this type. In each case the discrete wavelet family is a subframe of the continuous frame { Ψs,t}, and the discrete coefficient function is a sampled version of ƒ (s,t). The salient feature of discrete wavelet analysis is that the sampling rate is automatically adjusted to the scale. That means that a given signal is sampled by first dividing its frequency spectrum into "bands," quite analogous to musical scales in that corresponding frequencies on adjacent bands are related by a constant ratio δ > 1 (rather than a constant difference v > 0, as is the case for the discrete WFT). Then the signal in each band is sampled at a rate proportional to the frequency scale of that band, so that high-frequency bands get sampled at a higher rate than that of low-frequency bands. Under favorable conditions the signal can be reconstructed from such samples of its CWT as a discrete superposition of reciprocal wavelets.

Keywords

Discrete Wavelet Mother Wavelet Positive Scale Admissibility Condition Frame Bound 
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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