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This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets.  With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details.  From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification.  Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web.  Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient "overcomplete" wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems.  Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools.  The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic…is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology.

Mathematics. --- Fourier analysis. --- Computer mathematics. --- Numerical analysis. --- Numerical Analysis. --- Fourier Analysis. --- Computational Science and Engineering. --- Signal processing --- Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Computer science. --- Informatics --- Science --- Analysis, Fourier --- Mathematical analysis --- Computer mathematics --- Electronic data processing --- Mathematics

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This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India. .

Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Functional analysis. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Fourier Analysis. --- Signal, Image and Speech Processing. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Wavelets (Mathematics) --- Mathematical Analysis. --- Signal processing. --- Image processing. --- Speech processing systems. --- Math --- Science --- Wavelet analysis --- Harmonic analysis --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)