Some results in the theory modulated filter banks and modulated wavelet tight frames
type: Item
instance of: scholarly article
title: Some results in the theory modulated filter banks and modulated wavelet tight frames
zbMATH Open document ID: 0841.94001
author: Ramesh Gopinath
author: C. Sidney Burrus
published in: Applied and Computational Harmonic Analysis
publication date: 1996-07-23T00:00:00Z
review text: Perfect reconstruction filter banks, obtained by modulation of a linear-phase, low-pass, prototype filter, and the associated multichannel transmultiplexers are well documented in the engineering literature [\textit{N. J. Fliege}, Multirate digital signal processing: Multirate systems, filter banks, wavelets, Wiley (1995); \textit{R. A. Haddad}, \textit{T. W. Parsons}, Digital signal processing: Theory, applications, and hardware, Computer Science Press, New York, Oxford (1991); \textit{P. P. Vaidyanathan}, Multirate systems and filter banks, Prentice Hall (1993; Zbl 0784.93096); \textit{M. Vetterli} and \textit{J. Kovačević}, Wavelets and subband coding, Prentice Hall (1995)]. The filter bank techniques are of particular importance in speech analysis and synthesis by vocoder hardware which is remarkably immune to degradation from noise [\textit{R. A. Haddad} and \textit{T. W. Parsons} (loc. cit.)]. Another important application is in the field of high resolution radar imaging (SAR) and clinical magnetic resonance tomography [\textit{W. Schempp}, Wavelets in high resolution radar imaging and clinical magnetic resonance tomography. Cybern. Systems (to appear)]. Recently, perfect reconstruction modulated filter banks with the analysis and synthesis bank obtained from different prototypes have been reported. The paper under review describes a general form of modulation depending on an integer parameter, and presents a theory of modulated filter banks and associated wavelet bases including an efficient design procedure for unitary finite response modulated filter banks. Specifically, it deals with a parametrization of the unitary finite response modulated filter banks, and an associated parametrization of compactly supported modulated wavelet tight frames. A bewildering number of acronyms makes it hard to read the paper.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 94A13
zbMATH DE Number: 846190
zbMATH Keywords: modulation
zbMATH Keywords: modulated filter banks
zbMATH Keywords: wavelet bases
reviewed by: Walter Schempp
MaRDI profile type: Publication
full work available at URL: acha.1995.1023
OpenAlex ID: W1998941984
DOI: 10.1006/ACHA.1995.1023
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description: scientific article; zbMATH DE number 846190