Wavelet Transforms and Multirate Filtering

Wavelet Transforms and Multirate Filtering

Raghuveer Rao (Rochester Institute of Technology, USA)
Copyright: © 2002 |Pages: 19
DOI: 10.4018/978-1-930708-30-3.ch003
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Abstract

One of the most fascinating developments in the field of multirate signal processing has been the establishment of its link to the discrete wavelet transform. Indeed, it is precisely this link that has been responsible for the rapid application of wavelets in fields such as image compression. The objective of this chapter is to provide an overview of the wavelet transform and develop its link to multirate filtering. The birth of the field of wavelet transforms is now attributed to the seminal paper by Grossman and Morlet (1984) detailing the continuous wavelet transform or CWT. The CWT of a square integrable function is obtained by integrating it over regions defined by translations and dilations of a windowing function called the mother wavelet. The idea of representing functions or signals in terms of dilations can be found even in engineering articles dating back by several years, for example, Helstrom (1966). However, Grossman and Morlet’s formulation was more complete and was motivated by potential application to modeling seismic data. The next step of significance was the discovery of orthogonal wavelet basis functions and their role in defining multi-resolution representations (Daubechies 1988; Meyer 1992). Daubechies also provided a method for constructing compactly supported wavelets. Mallat (1989) established the fact that coefficients of orthogonal wavelet expansions can be obtained through multirate filtering which paved the way for widespread investigation of using wavelet transforms in signal and image processing applications. The objective of the chapter is to provide an overview of the relationship between multirate filtering and wavelet transformation. We begin with a brief account of the CWT, then go through the discrete wavelet transformation (DWT) followed by derivation of the relationship between the DWT and multirate filtering. The chapter concludes with an account of selected applications in digital image processing.

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Table of Contents
Preface
Gordana Jovanovic-Dolecek
Chapter 1
Gordana Jovanovic-Dolecek
This chapter treats the fundamentals of multirate system theory and includes decimation and interpolation as the basic concepts behind the changing... Sample PDF
Introduction to Multirate Systems
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Chapter 2
Tapio Saramaki, Robert Bregovic
During the last two decades, multirate filter banks have found various applications in many different areas, such as speech coding, scrambling... Sample PDF
Multirate Systems and Filterbanks
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Chapter 3
Raghuveer Rao
One of the most fascinating developments in the field of multirate signal processing has been the establishment of its link to the discrete wavelet... Sample PDF
Wavelet Transforms and Multirate Filtering
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Chapter 4
Ljiljana D. Milic, Miroslav D. Lutovac
Application of multirate techniques to improve digital filter design and implementation are considered in this chapter. FIR and IIR filter design... Sample PDF
Efficient Multirate Filtering
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Chapter 5
Godi Fischer
We begin our excursion into the field of data conversion by reviewing the most frequently applied conversion principles. The next section explains... Sample PDF
A/D Conversion Applications
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Chapter 6
Subband Coding of Signals  (pages 174-199)
Murilo B. de Carvalho, Eduardo A.B. da Silva
In this chapter we deal with subband coding of signals. We begin with an introduction to rate-distortion theory, and after that we discuss subband... Sample PDF
Subband Coding of Signals
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Chapter 7
Hector Perez-Meana, Mariko Nakano-Miyatake, Luis Nino-de-Rivera-y-Oyarzabal
This chapter reviews the basic principles of multirate adaptive filters together with some of their most successful applications, as well as some... Sample PDF
Speech and Audio Signal Applications
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Chapter 8
Cihan Tepedelenlioglu, Gerogios B. Giannakis
Multirate systems and filter banks have found many applications in source and channel coding over the last decade. This chapter addresses the design... Sample PDF
Applications of Filter Banks to Communications
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Chapter 9
Hakan Johansson, Lars Wanhammar
In this chapter we discuss techniques to design and implement multirate digital filters with low power consumption which also allow a reduction in... Sample PDF
Design and Implementation of Multirate Digital Filters
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About the Authors