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

The subject "optical signal processing" can and should include all aspects of optics and signal processing. However, that is too large a scope for a textbook that, like this one, is intended as an introduc tion to the subject at a level suitable for first year graduate students of electrical engineering, physics, and optical engineering. There fore, the subject matter has been restricted. The book begins with basic background material on optics, signal processing, matrix alge bra, ultrasound and SAWs, and CCDs. One might argue about this choice of topics. For example, there already exist very good books on matrix algebra. However, matrix algebra is so important in sig nal processing, especially in connection with devices such as optical matrix processors, that it was felt that a review was essential. Also, the matrix algebra needed for systolic arrays and parallel computing has made great advances in recent years. My original intention was to write a single-volume textbook cov ering most of the fundamental concepts and applications of optical signal processing. However, it soon became apparent that the large amount of material to be included would make publication in a single volume impracticable. Therefore this volume treats the "fundamen tals" and a second volume will appear dealing with devices and applications. This textbook was stimulated by a set of short courses that I have directed and lectured since 1976, as well as regular courses that I have taught at Rensselaer Polytechnic Institute since 1974."

Recently there has been intense research activity on the subject of wavelet/subband theory and application. Experts in such diverse fields as mathematics, physics, electrical engineering and image processing have provided original and pioneering works and results. But this diversity, while rich and productive, has lead to a sense of fragmentation, especially to those new to the field, and nonspecialists, trying to understand the connections between the different aspects of wavelet and subband theory.

The book is designed to present an understanding of wavelets and their development from a continuous-domain transformation to a frame representation and finally to multiresolution analysis tools such as subband decomposition. The book presents a theoretical understanding of the subject that is intertwined with practical examples and practical applications of wavelets in ultrasonic and biomedical applications. There is special emphasis on applications in communications and compression as well as image processing.

Topics and Features:

* Provides an understanding of the link between continuous wavelet transform, the fast wavelet transform and subband decomposition.

* Algorithms and numerical examples are implemented in Matlab.

* The design of wavelet bases, and how to implement the transform both in hardware and software is discussed in detail.

* Covers the fundamentals and the developments of the links between areas such as time-frequency analysis, digital signal processing, image processing and Fourier and wavelet transform, both continuous and discrete.

Extended mathematical treatment and numerous examples, with particular emphasis to the transition from thecontinuous domain to multiresolution and subband. The book is an essential text/reference for graduates, researchers, and professionals in electrical engineering, communications engineering and computer engineering. Practitioners and professionals engaged in signal processing, wavelets and Fourier analysis will find the book a useful resource and comprehensive guide.

A textbook on lasers and optical engineering should include all aspects of lasers and optics; however, this is a large undertaking. The objective of this book is to give an introduction to the subject on a level such that under graduate students (mostly juniors/seniors), from disciplines like electrical engineering, physics, and optical engineering, can use the book. To achieve this goal, a lot of basic background material, central to the subject, has been covered in optics and laser physics. Students with an elementary knowledge of freshman physics and with no formal courses in electromagnetic theory should be able to follow the book, although for some sections, knowledge of electromagnetic theory, the Fourier transform, and linear systems would be highly beneficial. There are excellent books on optics, laser physics, and optical engineering. Actually, most of my knowledge was acquired through these. However, when I started teaching an undergraduate course in 1974, under the same heading as the title of this book, I had to use four books to cover the material I thought an electrical engineer needed for his introduction to the world of lasers and optical engineering. In my sabbatical year, 1980-1981, I started writing class notes for my students, so that they could get through the course by possibly buying only one book. Eventually, these notes grew with the help of my undergraduate and graduate students, and the final result is this book."

A textbook on lasers and optical engineering should include all aspects of lasers and optics; however, this is a large undertaking. The objective of this book is to give an introduction to the subject on a level such that under graduate students (mostly juniors/seniors), from disciplines like electrical engineering, physics, and optical engineering, can use the book. To achieve this goal, a lot of basic background material, central to the subject, has been covered in optics and laser physics. Students with an elementary knowledge of freshman physics and with no formal courses in electromagnetic theory should be able to follow the book, although for some sections, knowledge of electromagnetic theory, the Fourier transform, and linear systems would be highly beneficial. There are excellent books on optics, laser physics, and optical engineering. Actually, most of my knowledge was acquired through these. However, when I started teaching an undergraduate course in 1974, under the same heading as the title of this book, I had to use four books to cover the material I thought an electrical engineer needed for his introduction to the world of lasers and optical engineering. In my sabbatical year, 1980-1981, I started writing class notes for my students, so that they could get through the course by possibly buying only one book. Eventually, these notes grew with the help of my undergraduate and graduate students, and the final result is this book."