| Description |
1 online resource (592 pages) |
| Contents |
Cover; Introduction to Orthogonal Transforms: With Applications in Data Processing and Analysis; Title; Copyright; Dedication; Contents; Preface; What is the book all about?; Why orthogonal transforms?; What is in the chapters?; Who are the intended readers?; About the homework problems and projects; Back to Euclid; Acknowledgments; Notation; General notation; 1: Signals and systems; 1.1 Continuous and discrete signals; 1.2 Unit step and nascent delta functions; 1.3 Relationship between complex exponentials and delta functions; 1.4 Attributes of signals |
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1.5 Signal arithmetics and transformations1.6 Linear and time-invariant systems; 1.7 Signals through continuous LTI systems; 1.8 Signals through discrete LTI systems; 1.9 Continuous and discrete convolutions; 1.10 Homework problems; 2: Vector spaces and signal representation; 2.1 Inner product space; 2.1.1 Vector space; 2.1.2 Inner product space; 2.1.3 Bases of vector space; 2.1.4 Signal representation by orthogonal bases; 2.1.5 Signal representation by standard bases; 2.1.6 An example: the Fourier transforms; 2.2 Unitary transformation and signal representation; 2.2.1 Linear transformation |
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2.2.2 Eigenvalue problems2.2.3 Eigenvectors of D2 as Fourier basis; 2.2.4 Unitary transformations; 2.2.5 Unitary transformations in N-D space; 2.3 Projection theorem and signal approximation; 2.3.1 Projection theorem and pseudo-inverse; 2.3.2 Signal approximation; 2.4 Frames and biorthogonal bases; 2.4.1 Frames; 2.4.2 Signal expansion by frames and Riesz bases; 2.4.3 Frames in finite-dimensional space; 2.5 Kernel function and Mercer's theorem; 2.6 Summary; 2.7 Homework problems; 3: Continuous-time Fourier transform; 3.1 The Fourier series expansion of periodic signals |
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3.1.1 Formulation of the Fourier expansion3.1.2 Physical interpretation; 3.1.3 Properties of the Fourier series expansion; 3.1.4 The Fourier expansion of typical functions; 3.2 The Fourier transform of non-periodic signals; 3.2.1 Formulation of the CTFT; 3.2.2 Relation to the Fourier expansion; 3.2.3 Properties of the Fourier transform; 3.2.4 Fourier spectra of typical functions; 3.2.5 The uncertainty principle; 3.3 Homework problems; 4: Discrete-time Fourier transform; 4.1 Discrete-time Fourier transform; 4.1.1 Fourier transform of discrete signals; 4.1.2 Properties of the DTFT |
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4.1.3 DTFT of typical functions4.1.4 The sampling theorem; 4.1.5 Reconstruction by interpolation; 4.2 Discrete Fourier transform; 4.2.1 Formulation of the DFT; 4.2.2 Array representation; 4.2.3 Properties of the DFT; 4.2.4 Four different forms of the Fourier transform; 4.2.5 DFT computation and fast Fourier transform; 4.3 Two-dimensional Fourier transform; 4.3.1 Two-dimensional signals and their spectra; 4.3.2 Fourier transform of typical 2-D functions; 4.3.3 Four forms of 2-D Fourier transform; 4.3.4 Computation of the 2-D DFT; 4.4 Homework problems; 5: Applications of the Fourier transforms |
| Summary |
A systematic, unified treatment of orthogonal transform methods that guides the reader from mathematical theory to problem solving in practice |
| Notes |
5.1 LTI systems in time and frequency domains |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Signal processing -- Digital techniques -- Mathematics.
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Transformations (Mathematics)
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Functions, Orthogonal.
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MATHEMATICS -- Functional Analysis.
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Functions, Orthogonal
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Signal processing -- Digital techniques -- Mathematics
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Transformations (Mathematics)
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| Form |
Electronic book
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| ISBN |
9781139220187 |
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1139220187 |
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9781139223614 |
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1139223615 |
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9781139015158 |
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113901515X |
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