Wavelets And Subbands

This book presents connections between the different aspects of wavelet and subband theory.

The scientists and engineers of today are relentless in their continuing study and analysis of the world about us from the microcosm to the macrocosm. A central purpose of this study is to gain sufficient scientific information and insight to enable the development of both representative and useful models of the superabundance of physical processes that surround us. The engineers need these models and the associated insight in order to build the information processing systems and control systems that comprise these new and emerging technologies. Much of the early modeling work that has been done on these systems has been based on the linear time-invariant system theory and its extensive use of Fourier transform theory for both continuous and discrete systems and signals. However many of the signals arising in nature and real systems are neither stationary nor linear but tend to be concentrated in both time and frequency. Hence a new methodology is needed to take these factors properly into account.

This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source. n The first book to give a unified and coherent exposition of multiresolutional signal decomposition techniques n Classroom tested textbook clearly describes the commonalities among three key methods-transform coding, and wavelet transforms n Gives comparative performance evaluations of many proposed techniques

A central goal of signal processing is to describe real-time signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. *provides broad coverage of theory and applications and a different perspective based on signal processing. *gives framework for applications in speech, audio, image and video compression as used in multimedia. *includes sufficient background material so that people without signal processing knowledge will find it useful.

The first book to provide a detailed discussion of the application of wavelets in wireless communications, this is an invaluable source of information for graduate students, researchers, and telecommunications engineers, managers and strategists. It overviews applications, explains how to design new wavelets and compares wavelet technology with existing OFDM technology. • Addresses the applications and challenges of wavelet technology for a range of wireless communication domains • Aids in the understanding of Wavelet Packet Modulation and compares it with OFDM • Includes tutorials on convex optimisation, spectral factorisation and the design of wavelets • Explains design methods for new wavelet technologies for wireless communications, addressing many challenges, such as peak-to-average power ratio reduction, interference mitigation, reduction of sensitivity to time, frequency and phase offsets, and efficient usage of wireless resources • Describes the application of wavelet radio in spectrum sensing of cognitive radio systems.

Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on “wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students.

This book traces the prehistory and initial development of wavelet theory, a discipline that has had a profound impact on mathematics, physics, and engineering. Interchanges between these fields during the last fifteen years have led to a number of advances in applications such as image compression, turbulence, machine vision, radar, and earthquake prediction. This book contains the seminal papers that presented the ideas from which wavelet theory evolved, as well as those major papers that developed the theory into its current form. These papers originated in a variety of journals from different disciplines, making it difficult for the researcher to obtain a complete view of wavelet theory and its origins. Additionally, some of the most significant papers have heretofore been available only in French or German. Heil and Walnut bring together these documents in a book that allows researchers a complete view of wavelet theory's origins and development.

Although there have been numerous books on wavelet applications to various scientific disciplines, this cutting-edge, practical book is the first to concentrate on wavelet applications to remote sensing and subsurface sensing from an engineer's point of view. The book introduces you to wavelet transform uses in a wide range of sensing technologies, demonstrates the usefulness of combining the wavelet transform with other signal processing tools to solve complicated sensing technology problems, and features several time-saving algorithms and Matlab® codes that help you with your specific projects in the field.