An introduction to wavelets through linear algebra
- 作者: Frazier, Michael,
- 出版: New York : Springer ©1999.
- 稽核項: 1 online resource (xvi, 501 pages).
- 叢書名: Undergraduate texts in mathematics
- 標題: Lineaire algebra. , Infinity. , Wavelets (Mathematics) , Ondelettes. , Algèbre linéaire. , Electronic books. , Fourier, Analyse de. , Wavelets. , Fourier-analyse. , Algebras, Linear. , Análise de ondaletas (wavelets) , MATHEMATICS , MATHEMATICS Infinity. , Álgebra linear.
- ISBN: 3642855709 , 9783642855702
- ISBN: 0387986391 , 9780387986395
- 試查全文@TNUA:
- 附註: Includes bibliographical references (pages 484-490) and index. Cover -- Preface -- Acknowledgments -- Table of Contents -- Prologue: Compression of the FBI Fingerprint Files -- 1. Background: Complex Numbers and Linear Algebra -- 2. The Discrete Fourier Transform -- 3. Wavelets on ZN -- 4. Wavelets on Z -- 5. Wavelets on R -- 6. Wavelets and Differential Equations -- Bibliography.
- 摘要: "This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given." "This text is ideal for a topics course for mathematics majors, because it exhibits an emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets."--Jacket.
- 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=104553
- 系統號: 005307183
- 資料類型: 電子書
- 讀者標籤: 需登入
- 引用網址: 複製連結
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.
來源: Google Book
來源: Google Book
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