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An Introduction to Wavelets Through Linear Algebra

  • Textbook
  • © 1999

Overview

Authors:
  1. Michael W. Frazier

    1. Department of Mathematics, Michigan State University, East Lansing, USA

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  • This introduction to wavelets thoroughly covers the basics of the theory Shows non-trivial mathematics leading to natural and important applications, such as video compression and numerical solution of differential equations Includes an interesting prologue which explains the use of wavelet compression in storing the FBIs fingerprint files Requires only a basic linear algebra background along with a bit of analysis Wavelets are a hot area of modern mathematical research
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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Prologue: Compression of the FBI Fingerprint Files

    Pages 1-6

  3. Background: Complex Numbers and Linear Algebra

    Pages 7-100

  4. The Discrete Fourier Transform

    Pages 101-164

  5. Wavelets on Z N

    Pages 165-263

  6. Wavelets on Z

    Pages 265-348

  7. Wavelets on R

    Pages 349-450

  8. Wavelets and Differential Equations

    Pages 451-483

  9. Back Matter

    Pages 484-505
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Keywords

About this book

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. Basicwavelettheoryisanaturaltopicforsuchacourse. Byname, 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 suf?ciently 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. These are introduced in the ?rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de?nitions in sections 1. 3 and 1. 4. From our viewpoint, linear transformations are the primary object of study; v Preface vi a matrix arises as a realization of a linear transformation. Many students may have been exposed to the material on change of basis in section 1. 4, but may bene?t from seeing it again. In section 1.

Authors and Affiliations

  • Department of Mathematics, Michigan State University, East Lansing, USA

    Michael W. Frazier

Bibliographic Information

  • Book Title: An Introduction to Wavelets Through Linear Algebra

  • Authors: Michael W. Frazier

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/b97841

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 1999

  • Hardcover ISBN: 978-0-387-98639-5Published: 11 June 1999

  • Softcover ISBN: 978-1-4757-7299-9Published: 23 March 2013

  • eBook ISBN: 978-0-387-22653-8Published: 06 April 2006

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XVI, 503

  • Topics: Analysis, Algebra, Numerical Analysis

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