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Discrete-Time Wavelets

  • Miloš Doroslovački
Part of the Computational Imaging and Vision book series (CIVI, volume 19)

Abstract

The intention of this paper is to provide an elementary introduction to the subject of discrete-time wavelets. It defines the discrete-time wavelets and reviews their properties in a systematic and consistent way. Different kinds of orthogonality between the wavelets are addressed and the corresponding sufficient and necessary conditions are derived. It is shown when discrete-time wavelets can be samples of continuous-time wavelets. The conditions for shift-invariance of discrete-time wavelet representations are given in detail. The appearance of two biorthogonal representation sets of discrete-time wavelets from the binary subband decomposition/reconstruction of signals is pointed out. When the number of different representation scales is finite, it is shown that in order to obtain the orthogonality between wavelets, the known requirement for wavelet generating filter can be relaxed.

Keywords

Filter Bank Perfect Reconstruction Orthonormal Wavelet Reconstruction Filter Subband Decomposition 
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

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Miloš Doroslovački
    • 1
  1. 1.Department of Electrical and Computer EngineeringThe George Washington UniversityWashintonUSA

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