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Proceedings Paper

Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors
Author(s): İlker Bayram; Ivan W. Selesnick
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Paper Abstract

Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for time-scale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechies-type filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet wavelet transforms (tight frames) with FIR filters obtained using matrix spectral factorization.

Paper Details

Date Published: 2 October 2007
PDF: 15 pages
Proc. SPIE 6763, Wavelet Applications in Industrial Processing V, 67630H (2 October 2007); doi: 10.1117/12.741073
Show Author Affiliations
İlker Bayram, Polytechnic Univ. (United States)
Ivan W. Selesnick, Polytechnic Univ. (United States)

Published in SPIE Proceedings Vol. 6763:
Wavelet Applications in Industrial Processing V
Frédéric Truchetet; Olivier Laligant, Editor(s)

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