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Nonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems.To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas:

Time-series analysis --- Nonlinear theories --- Nonlinear theories. --- Time-series analysis. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Analysis of time series --- Calculus --- Mathematical analysis --- Mathematical physics --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities

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Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets.  Written at the level of a first course in calculus and linear algebra, its accessible presentation is designed for undergraduates in a variety of disciplines—computer science, engineering, mathematics, mathematical sciences—as well as for practicing professionals in these areas.    The present softcover reprint retains the corrections from the second printing (2001) and makes this unique text available to a wider audience. The first chapter starts with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.   The second part of this book provides the foundations of least-squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets.   Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.

Wavelets (Mathematics) --- 519.6 --- 519.65 --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Wavelet analysis --- Harmonic analysis --- Wavelets (Mathematics). --- Civil & Environmental Engineering --- Operations Research --- Applied Mathematics --- 517.518.8 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Ondelettes --- Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Electrical engineering. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Electrical Engineering. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Algebra --- Harmonic analysis. Fourier analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Computer engineering. --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Computers --- Analysis, Fourier --- Design and construction --- Ondelettes. --- Engineering --- Engineering analysis --- Electric engineering --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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Groups & Geometric Analysis

Lie groups. --- Geometry, Differential. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Geometry, Differential --- Lie groups --- 517.986.6 --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- Harmonic analysis of functions of groups and homogeneous spaces --- Groupes compacts. --- Compact groups --- Integral transforms --- Transformations intégrales --- Radon transforms. --- Radon, Transformations de. --- Meetkunde (Differentiaal-) --- Algèbres de Lie. --- Géométrie différentielle --- Lie (Algebra's van). --- Géometrie différentielle --- Géometrie intégrale --- Géometrie différentielle --- Géometrie intégrale --- Radon, Transformations de --- Analyse harmonique --- Analyse sur une variété

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Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas

Seismic reflection method --- Petroleum --- Time-series analysis --- Natural gas --- Deconvolution --- Time-series analysis. --- Petroleum. --- Natural gas. --- Gas, Natural --- Sour gas --- Gases, Asphyxiating and poisonous --- Hydrocarbons --- Coal-oil --- Crude oil --- Oil --- Caustobioliths --- Mineral oils --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities --- Deconvolution in seismic reflection --- Deconvolution. --- Data processing --- Pétrole --- Gaz naturel --- Prospection. --- Prospecting --- Géologie. --- Geology --- Prospection --- Géologie --- Seismic reflection method - Deconvolution

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An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Fourier series. --- Fourier series --- 517.518.4 --- 517.518.5 --- 517.51 --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral --- 517.51 Functions of a real variable. Real functions --- Functions of a real variable. Real functions --- 517.518.4 Trigonometric series --- Acqui 2006