Introduction to Orthogonal Transforms : With Applications in Data Processing and Analysis.

Print version record.

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.

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.

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.

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.

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.

5.1 LTI systems in time and frequency domains.

A systematic, unified treatment of orthogonal transform methods that guides the reader from mathematical theory to problem solving in practice.

Includes bibliographical references and index.

eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - Worldwide