Multiwavelet bases with extra approximation properties

Research output: Contribution to journalArticle

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 preceded by a preprocessing step (preflltering). 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), prefltering can be avoided. By reorganizing the multiwavelet (vector) filter bank as a multichannel scalar filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. A main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by 0~2r - i)/(z-1 - 1).

Original languageEnglish (US)
Pages (from-to)542
Number of pages1
JournalIEEE Transactions on Signal Processing
Volume46
Issue number2
StatePublished - 1998

Fingerprint

Filter banks
Transfer functions
Signal processing

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Multiwavelet bases with extra approximation properties. / Selesnick, Ivan.

In: IEEE Transactions on Signal Processing, Vol. 46, No. 2, 1998, p. 542.

Research output: Contribution to journalArticle

@article{737febf193a846b88da35ea4ca93981f,
title = "Multiwavelet bases with extra approximation properties",
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 preceded by a preprocessing step (preflltering). 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), prefltering can be avoided. By reorganizing the multiwavelet (vector) filter bank as a multichannel scalar filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. A main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by 0~2r - i)/(z-1 - 1).",
author = "Ivan Selesnick",
year = "1998",
language = "English (US)",
volume = "46",
pages = "542",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",

}

TY - JOUR

T1 - Multiwavelet bases with extra approximation properties

AU - Selesnick, Ivan

PY - 1998

Y1 - 1998

N2 - 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 preceded by a preprocessing step (preflltering). 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), prefltering can be avoided. By reorganizing the multiwavelet (vector) filter bank as a multichannel scalar filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. A main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by 0~2r - i)/(z-1 - 1).

AB - 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 preceded by a preprocessing step (preflltering). 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), prefltering can be avoided. By reorganizing the multiwavelet (vector) filter bank as a multichannel scalar filter bank, the development in this paper draws from results regarding the approximation order of M-band wavelet bases. A main result thereby obtained is a characterization of balanced multiwavelet bases in terms of the divisibility of certain transfer functions by 0~2r - i)/(z-1 - 1).

UR - http://www.scopus.com/inward/record.url?scp=33747802779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747802779&partnerID=8YFLogxK

M3 - Article

VL - 46

SP - 542

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 2

ER -