@inproceedings{6a1b5a9edc354bbb8841da6c23cb3e9b,
title = "Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors",
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 Gr{\"o}bner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.",
keywords = "Frames, Overcomplete filter banks, Rational filter banks, Rational wavelets",
author = "Ilker Bayram and Selesnick, {Ivan W.}",
year = "2007",
doi = "10.1117/12.741073",
language = "English (US)",
isbn = "9780819469236",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
booktitle = "Wavelet Applications in Industrial Processing V",
note = "Wavelet Applications in Industrial Processing V ; Conference date: 11-09-2007 Through 12-09-2007",
}