An Introduction to Wavelets

An Introduction to Wavelets
Author: Charles K. Chui
Publsiher: Elsevier
Total Pages: 278
Release: 2016-06-03
Genre: Science
ISBN: 9781483282862

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Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on “wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students.

An Introduction to Wavelets Through Linear Algebra

An Introduction to Wavelets Through Linear Algebra
Author: M.W. Frazier
Publsiher: Springer
Total Pages: 517
Release: 2013-12-11
Genre: Mathematics
ISBN: 9783642855702

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Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.

An Introduction to Wavelet Analysis

An Introduction to Wavelet Analysis
Author: David F. Walnut
Publsiher: Springer Science & Business Media
Total Pages: 453
Release: 2013-12-11
Genre: Computers
ISBN: 9781461200017

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This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

An Introduction to Wavelets and Other Filtering Methods in Finance and Economics

An Introduction to Wavelets and Other Filtering Methods in Finance and Economics
Author: Ramazan Gençay,Faruk Selçuk,Brandon J. Whitcher
Publsiher: Elsevier
Total Pages: 359
Release: 2001-10-12
Genre: Education
ISBN: 9780080509228

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An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method. The first book to present a unified view of filtering techniques Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series Provides easy access to a wide spectrum of parametric and non-parametric filtering methods

Introduction to Wavelets and Wavelet Transforms

Introduction to Wavelets and Wavelet Transforms
Author: C. S. Burrus,Ramesh A. Gopinath,Haitao Guo
Publsiher: Pearson
Total Pages: 294
Release: 1998
Genre: Mathematics
ISBN: STANFORD:36105019319495

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Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.

A Mathematical Introduction to Wavelets

A Mathematical Introduction to Wavelets
Author: P. Wojtaszczyk
Publsiher: Cambridge University Press
Total Pages: 280
Release: 1997-02-13
Genre: Mathematics
ISBN: 0521578949

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The only introduction to wavelets that doesn't avoid the tough mathematical questions.

Real Analysis with an Introduction to Wavelets and Applications

Real Analysis with an Introduction to Wavelets and Applications
Author: Don Hong,Jianzhong Wang,Robert Gardner
Publsiher: Elsevier
Total Pages: 387
Release: 2004-12-31
Genre: Mathematics
ISBN: 9780080540313

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Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications. The text is relatively elementary at the start, but the level of difficulty steadily increases The book contains many clear, detailed examples, case studies and exercises Many real world applications relating to measure theory and pure analysis Introduction to wavelet analysis

An Introduction to Wavelet Theory in Finance

An Introduction to Wavelet Theory in Finance
Author: Francis In,Sangbae Kim
Publsiher: World Scientific
Total Pages: 213
Release: 2013
Genre: Business & Economics
ISBN: 9789814397834

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This book offers an introduction to wavelet theory and provides the essence of wavelet analysis including Fourier analysis and spectral analysis; the maximum overlap discrete wavelet transform; wavelet variance, covariance, and correlation in a unified and friendly manner. It aims to bridge the gap between theory and practice by presenting substantial applications of wavelets in economics and finance. This book is the first to provide a comprehensive application of wavelet analysis to financial markets, covering new frontier issues in empirical finance and economics. The first chapter of this unique text starts with a description of the key features and applications of wavelets. After an overview of wavelet analysis, successive chapters rigorously examine the various economic and financial topics and issues that stimulate academic and professional research, including equity, interest swaps, hedges and futures, foreign exchanges, financial asset pricing, and mutual fund markets. This detail-oriented text is descriptive and designed purely for academic researchers and financial practitioners. It assumes no prior knowledge of econometrics and covers important topics such as portfolio asset allocation, asset pricing, hedging strategies, new risk measures, and mutual fund performance. Its accessible presentation is also suitable for post-graduates in a variety of disciplines applied economics, financial engineering, international finance, financial econometrics, and fund management. To facilitate the subject of wavelets, sophisticated proofs and mathematics are avoided as much as possible when applying the wavelet multiscaling method. To enhance the reader's understanding in practical applications of the wavelet multiscaling method, this book provides sample programming instruction backed by Matlab wavelet code.