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Full Description
Recently there has been intense research activity on the subject
of wavelet and subband theory. Experts in diverse fields such as
mathematics, physics, electrical engineering, and image processing
have provided original and pioneering works and results. But this
diversity, while rich and productive, has led to a sense of
fragmentation, especially to those new to the field and to
nonspecialists who are trying to understand the connections between
the different aspects of wavelet and subband theory.
`Wavelets and Subbands' 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 applications of wavelets in
ultrasonic and biomedical domains. There is special emphasis on
applications in communications, compression, and image processing.
Topics and Features: * Provides an understanding of the link
between the continuous wavelet transform, the fast wavelet transform,
and subband decomposition * Algorithms and numerical examples are
implemented in MATLAB * Discusses the design of wavelet bases and
details how to implement the transform both in hardware and software *
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 * Offers extended mathematical treatment and numerous
examples, with particular emphasis on the transition from the
continuous domain to multiresolution and subband decomposition.
The book is an essential text and reference for graduates,
researchers, and professionals in electrical engineering,
Contents
1. Introduction.- 1.1 Historical Review: From Fourier Analysis to Wavelet Analysis and Subband.- 1.2 Organization of This Book.- 1.3 References.- I: Fundamentals.- 2. Wavelet Fundamentals.- II: Wavelets and Subbands.- 3. Time and Frequency Analysis of Signals.- 4. Discrete Wavelet Transform: From Frames to Fast Wavelet Transform.- 5. Theory of Subband Decomposition.- 6. Two-Dimensional Wavelet Transforms and Applications.- III: Applications.- 7. Applications of Wavelets in the Analysis of Transient Signals.- 8. Applications of Subband and Wavelet Transform in Communication Systems.- 9. Real-Time Implementations of Wavelet Transforms.- A. Fourier Transform.- B. Discrete Fourier Transform.- C. z-Transform.- D. Orthogonal Representation of Signals.
