DocumentCode :
1440941
Title :
Multiwavelet bases with extra approximation properties
Author :
Selesnick, Ivan W.
Author_Institution :
Dept. of Electr. Eng., Polytech. Univ., Brooklyn, NY, USA
Volume :
46
Issue :
11
fYear :
1998
fDate :
11/1/1998 12:00:00 AM
Firstpage :
2898
Lastpage :
2908
Abstract :
This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step (prefiltering). This paper examines the properties and design of orthogonal multiwavelet bases, with approximation order >1 that possess those properties that are normally absent. For these “balanced” bases (so named by Lebrun and Vetterli (see Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Munich, Germany, vol.3, p.2473-76, 1997 and ibid., vol.46, p.1119-24, 1998)), prefiltering can be avoided. By reorganizing the multiwavelet filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. The main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by powers of (z-2r-1)/(z-1-1). For traditional wavelets (r=1), this specializes to the usual factor (z+1) K
Keywords :
approximation theory; band-pass filters; filtering theory; signal processing; transfer functions; wavelet transforms; approximation order; approximation properties; multiwavelet filter bank; orthogonal multiwavelet bases design; prefiltering; preprocessing step; signal processing; transfer functions divisibility; Discrete wavelet transforms; Filter bank; Filtering theory; Polynomials; Signal processing; Transfer functions; Wavelet transforms;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.726804
Filename :
726804
Link To Document :
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