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Harmonic analysis. Fourier analysis

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Topological groups. Lie groups --- Harmonic analysis. Fourier analysis

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Fourier analysis --- Fourier analysis. --- Mathematical models. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Fourier Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computational Science and Engineering. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Analysis, Fourier

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This book is an outgrowth of courses given by me for graduate students at York University in the past ten years. The actual writing of the book in this form was carried out at York University, Peking University, the Academia Sinica in Beijing, the University of California at Irvine, Osaka University, and the University of Delaware. The idea of writing this book was ?rst conceived in the summer of 1989, and the protracted period of gestation was due to my daily duties as a professor at York University. I would like to thank Professor K. C. Chang, of Peking University; Professor Shujie Li, of the Academia Sinica in Beijing; Professor Martin Schechter, of the University of California at Irvine; Professor Michihiro Nagase, of Osaka University; and Professor M. Z. Nashed, of the University of Delaware, for providing me with stimulating environments for the exchange of ideas and the actual writing of the book. We study in this book the properties of pseudo-differential operators arising in quantum mechanics, ?rst envisaged in [33] by Hermann Weyl, as bounded linear 2 n operators on L (R ). Thus, it is natural to call the operators treated in this book Weyl transforms.

Fourier analysis --- Pseudodifferential operators --- Fourier analysis. --- Pseudodifferential operators. --- Mathematics. --- Topological groups. --- Lie groups. --- Topological Groups, Lie Groups. --- Topological Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Analysis, Fourier --- Mathematical analysis --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory

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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. .

Harmonic analysis. Fourier analysis --- 517.518.8 --- 519.6 --- Approximation of functions by polynomials and their generalizations --- Computational mathematics. Numerical analysis. Computer programming --- Signal processing --- Wavelets (Mathematics) --- Mathematics. --- Wavelets (Mathematics). --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Wavelet analysis --- Harmonic analysis --- Mathematics --- Fourier analysis. --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Signal processing. --- Image processing. --- Speech processing systems. --- Electrical engineering. --- Fourier Analysis. --- Computational Mathematics and Numerical Analysis. --- Mathematical and Computational Engineering. --- Signal, Image and Speech Processing. --- Communications Engineering, Networks. --- Computational Science and Engineering. --- Electric engineering --- Engineering --- 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) --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Electronic data processing --- Analysis, Fourier