Conceptual Wavelets In Digital Signal Processing

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

This textbook is unique because of its in-depth treatment of the applications of wavelets and wavelet transforms to many areas, across many disciplines. The book is written to serve the needs of a one or two semester course at either the undergraduate or graduate level. The author uses a very simplified, accessible approach that de-emphasizes mathematical rigor. The presentation includes many diagrams to illustrate points being discussed and uses MATLAB for all of application code. The author reinforces concepts introduced in the book with easy to grasp review questions and problems, tailored to each specific chapter for better mastery of the subject matter. This book enables students to understand the fundamental concepts of wavelets and wavelet transforms, as well as how to use them for problem solutions in digital signal and image processing, mixed-signal testing, space applications, aerospace applications, biomedical, cyber security, homeland security and many other application areas. Provides textbook coverage of Wavelets and applications, suitable for one and two semester courses, either at the undergraduate or graduate level; Discusses many types of wavelets and their applications across many disciplines; Includes MATLAB code illustrations to simplify the understanding of the various applications; Uses many illustrations, figures, tables, and visual comparisons to simplify and clarify the various concepts of wavelets, wavelet transforms and the various application areas; Ends each chapter with review questions/answers, as well as exercises to reinforce and test concepts introduced; Solutions manual and PowerPoint slides for each chapter available for instructors.

Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research.

How signal processing works: clear, simple explanations in plain English Breakthrough DSP applications: from smartphones to healthcare and beyond Covers both digital and analog signals An indispensable resource for tech writers, marketers, managers, and other nonengineers The Complete DSP Guide for Businesspeople and Nontechnical Professionals Digital signal processing (DSP) technology is everywhere–each time you use a smartphone, tablet, or computer; play an MP3; watch a digital TV or DVD; get GPS directions; play a video game; take a digital photo; or even have an MRI, DSP technology is at work. Now, for the first time, The Essential Guide to Digital Signal Processing offers readers of all levels simple, plain-English explanations of digital and analog signals and modern DSP applications. Whether you sell technology, write about it, manage it, fix it, or invest in it, this is the book for you. Using everyday examples and simple diagrams, two leading DSP consultants and instructors completely demystify signal processing. You’ll discover what digital signals are, how they’re generated, and how they’re changing your life. You’ll learn all you need to know about digital signal collection, filtering, analysis, and more, and how DSP works in today’s most exciting devices and applications. Coverage includes How engineers understand and work with analog signal spectra and frequencies How digital signals are generated and used in modern electronic devices The surprising things that happen when analog signals are converted to digital form How (and why) engineers compute digital signal spectra with Fourier transforms What wavelets are and how they’re used everywhere, from medicine to the camera in your smartphone How digital filters are used in DSP applications Cutting-edge DSP applications, from automatic music-tuning software to medical EKG signal analysis A comprehensive glossary of signal processing terminology and acronyms You’ll gain a clear, conceptual understanding of all key signal processing operations and vocabulary. That means you’ll understand much of the “magic” built into today’s newest devices, and you’ll be ready to succeed in virtually any nontechnical role that requires DSP knowledge.

The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.