The method of wavelet transforms is one key tool in signal processing and control. Modern wavelet theory defines outlines for construction of wavelets and transformations using them. It gives rules that one has to obey to get a wavelet basis with desired properties, meaning that everyone can create a wavelet adequate for the given task. An oscillatory property and multiresolution nature of wavelets recommends them for use both in signal processing and in solving complex mathematical models of real world phenomena.
This book brings to engineers and other practitioners help in understanding how wavelets work in order to be able to create new or modify the existing wavelets according to their needs and tries to satisfy different user groups. It is self contained and no previous knowledge is assumed.
In seven chapters, the book gives a concise understanding of the theory of wavelets, explains how to compute them in practise and finally presents typical applications of wavelets and how they work. The book is written for graduate students and practising Engineers of electrical communications, signal processing and control.
Autorentext
Zusammenfassung
Real world phenomena are permanently changing with various speeds of change. Repeating of four seasons in a year accompanied by appropriate changes in nature, alternation of day and night within twenty four hours, heart pulsations, air vibra tions that produce sound or stock-market fluctuations are only several examples. Furthermore, since most of these problems express nonlinear effects characterized by fast and short changes, small waves or wavelets are an ideal modeling tool. An oscillatory property and multiresolution nature of wavelets recommends them for use both in signal processing and in solving complex mathematical models of real world phenomena. As a professor at the School of Mathematics, who teaches computer science students, I feel the need to bridge' the gap between the theoretical and practical aspects of wavelets. On the one side, mathematicians need help to implement wavelet theory in solving practical problems. On the other side, engineers and other practitioners need help in understanding how wavelets work in order to be able to create new or modify the existing wavelets according to their needs. This book tries to satisfy both wavelet user groups; to present and explain the mathematical bases of the wavelet theory and to link them with some of the a~eas where this theory is already being successfully applied. It is self contained and no previous knowledge is assumed. The introductory chapter gives a short overview of the development of the wavelet concept from its origins at the beginning ofthe twentieth century until now.
Inhalt
Least-squares approximation.- Multiresolution.- Wavelets.- How to compute.- Analogy with filters.- Applications.