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An introduction to wavelets through linear algebra

Author: Michael W Frazier
Publisher: New York, NY [u.a.] : Springer, 1999.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Intended to be as  Read more...

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Genre/Form: Einführung
Lehrbuch
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michael W Frazier
ISBN: 0387986391 9780387986395
OCLC Number: 245985370
Notes: Literaturverz. S. 484 - 490.
Description: XVI, 501 S : ill., graph. Darst.
Contents: Preface Acknowledgments Prologue: Compression of the FBI Fingerprint Files 1 Background: Complex Numbers and Linear Algebra 1.1 Real Numbers and Complex Numbers 1.2 Complex Series, Euler's Formula, and the Roots of Unity 1.3 Vector Spaces and Bases 1.4 Linear Transformations, Matrices, and Change of Basis 1.5 Diagonalization of Linear Transformations and Matrices 1.6 Inner Products, Orthonormal Bases, and Unitary Matrices 2 The Discrete Fourier Transform 2.1 Basic Properties of the Discrete Fourier Transform 2.2 Translation-Invariant Linear Transformations 2.3 The Fast Fourier Transform 3 Wavelets on $bZ_N$ 3.1 Construction of Wavelets on $bZ_N$: The First Stage 3.2 Construction of Wavelets on $bZ_N$: The Iteration Step 3.3 Examples and Applications 4 Wavelets on $bZ$ 4.1 $\ell ^2(bZ)$ 4.2 Complete Orthonormal Sets in Hilbert Spaces 4.3 $L^2([-\pi ,\pi ))$ and Fourier Series 4.4 The Fourier Transform and Convolution on $\ell ^2(bZ)$ 4.5 First-Stage Wavelets on $bZ$ 4.6 The Iteration Step for Wavelets on $bZ$ 4.7 Implementation and Examples 5 Wavelets on $bR$ 5.1 $L^2(bR)$ and Approximate Identities 5.2 The Fourier Transform on $bR$ 5.3 Multiresolution Analysis and Wavelets 5.4 Construction of Multiresolution Analyses 5.5 Wavelets with Compact Support and Their Computation 6 Wavelets and Differential Equations 6.1 The Condition Number of a Matrix 6.2 Finite Difference Methods for Differential Equations 6.3 Wavelet-Galerkin Methods for Differential Equations Bibliography Index
Series Title: Undergraduate texts in mathematics.
Responsibility: Michael W. Frazier.
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