Synopsis
Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.
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From the Back Cover
This volume is designed as a new source for modern topics dealing with wavelets, wavelet transforms time-frequency signal analysis and other applications for future development of this new, important and useful subject for mathematics, science and engineering. Its main features include:
A broad coverage of recent material on wavelet analysis, and time-frequency signal analysis and other applications that are not usually covered in other recent reference books.
The material presented in this volume brings together a rich variety of ideas that blend most aspects of the subject mentioned above.
This volume brings together a detailed account of major recent developments in wavelets, wavelet transforms and time-frequency signal analysis.
This volume provides the reader with a thorough mathematical background and a wide variety of applications that are sufficient to do interdisciplinary collaborative research in applied mathematics.
The book provides information that puts the reader at the forefront of the current resarch. An up-to-date bibliography is included at the end of each chapter to stimulate new interest in future study and research.
About the Author
Lokenath Debnath, Ph.D., is a Professor of Mathematics at The University of Texas-Pan American. He received his Ph.D. in Applied Mathematics from the University of London, and a Ph.D. in Pure Mathematics from the University of Calcutta. His areas of interest are applied mathematics, applied partial differential equations, integral transforms, fluid dynamics, and continuum mechanics. Firdous Ahmad Shah, Ph.D., is an Assistant Professor in the Post Graduate Department of Mathematics at the University of Kashmir. His areas of specialization are: wavelets, wavelet packets, applications of wavelets in financial time series, and wavelet neural networks.
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