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Discrete-Time Wavelets

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Book cover Wavelets in Signal and Image Analysis

Part of the book series: Computational Imaging and Vision ((CIVI,volume 19))

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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.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The George Washington University, Washinton, DC, 20052, USA

    Miloš Doroslovački

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  1. Miloš Doroslovački
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Editor information

Editors and Affiliations

  1. Texas Tech University, Lubbock, Texas, USA

    Arthur A. Petrosian

  2. University of Colorado, Boulder, Colorado, USA

    François G. Meyer

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© 2001 Springer Science+Business Media Dordrecht

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Doroslovački, M. (2001). Discrete-Time Wavelets. In: Petrosian, A.A., Meyer, F.G. (eds) Wavelets in Signal and Image Analysis. Computational Imaging and Vision, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9715-9_1

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  • DOI: https://doi.org/10.1007/978-94-015-9715-9_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5838-6

  • Online ISBN: 978-94-015-9715-9

  • eBook Packages: Springer Book Archive

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