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Signal Analysis: Time, Frequency, Scale, and Structure [Hardback]

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  • Format: Hardback, 960 pages, height x width x depth: 241x160x50 mm, weight: 1379 g, Drawings: 200 B&W, 0 Color
  • Pub. Date: 20-Jan-2004
  • Publisher: Wiley-IEEE Press
  • ISBN-10: 0471234419
  • ISBN-13: 9780471234418
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Signal Analysis: Time, Frequency, Scale, and StructureLarger Image
  • Format: Hardback, 960 pages, height x width x depth: 241x160x50 mm, weight: 1379 g, Drawings: 200 B&W, 0 Color
  • Pub. Date: 20-Jan-2004
  • Publisher: Wiley-IEEE Press
  • ISBN-10: 0471234419
  • ISBN-13: 9780471234418
Other books in subject:
Permanent link: https://www.kriso.lv/db/9780471234418.html
Keywords:
This text for undergraduate science and engineering students provides a gradual introduction to the theory behind signal analysis as well as the abstract mathematics and functional analysis related to signal analysis. Written to be accessible to readers of different levels of mathematical background, the text clarifies basic concepts and types of signals and progresses to the mathematics of Hilbert spaces, complex analysis, distributions, and analog Fourier transforms. Chapter problems are included. Allen received a PhD in computer science from the University of Texas-Arlington. Mills received a PhD in electrical engineering from the University of Texas-Dallas. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

  • Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods
  • Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques
  • Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis
  • Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Preface xvii
Acknowledgments xxi
Signals: Analog, Discrete, and Digital
1(108)
Introduction to Signals
4(17)
Basic Concepts
4(7)
Time-Domain Description of Signals
11(7)
Analysis in the Time-Frequency Plane
18(2)
Other Domains: Frequency and Scale
20(1)
Analog Signals
21(14)
Definitions and Notation
22(1)
Examples
23(9)
Special Analog Signals
32(3)
Discrete Signals
35(5)
Definitions and Notation
35(2)
Examples
37(2)
Special Discrete Signals
39(1)
Sampling and Interpolation
40(11)
Introduction
40(2)
Sampling Sinusoidal Signals
42(1)
Interpolation
42(4)
Cubic Splines
46(5)
Periodic Signals
51(12)
Fundamental Period and Frequency
51(4)
Discrete Signal Frequency
55(1)
Frequency Domain
56(6)
Time and Frequency Combined
62(1)
Special Signal Classes
63(7)
Basic Classes
63(2)
Summable and Integrable Signals
65(1)
Finite Energy Signals
66(1)
Scale Description
67(1)
Scale and Structure
67(3)
Signals and Complex Numbers
70(8)
Introduction
70(1)
Analytic Functions
71(4)
Complex Integration
75(3)
Random Signals and Noise
78(14)
Probability Theory
79(5)
Random Variables
84(7)
Random Signals
91(1)
Summary
92(17)
Historical Notes
93(2)
Resources
95(1)
Looking Forward
96(1)
Guide to Problems
96(1)
References
97(3)
Problems
100(9)
Discrete Systems and Signal Spaces
109(64)
Operations on Signals
110(12)
Operations on Signals and Discrete Systems
111(10)
Operations on Systems
121(1)
Types of Systems
121(1)
Linear Systems
122(5)
Properties
124(1)
Decomposition
125(2)
Translation Invariant Systems
127(1)
Convolutional Systems
128(8)
Linear, Translation-Invariant Systems
128(2)
Systems Defined by Difference Equations
130(1)
Convolution Properties
131(2)
Application: Echo Cancellation in Digital Telephony
133(3)
The lp Signal Spaces
136(13)
lp Signals
137(1)
Stable Systems
138(1)
Toward Abstract Signal Spaces
139(3)
Normed Spaces
142(5)
Banach Spaces
147(2)
Inner Product Spaces
149(9)
Definitions and Examples
149(2)
Norm and Metric
151(2)
Orthogonality
153(5)
Hilbert Spaces
158(10)
Definitions and Examples
158(1)
Decomposition and Direct Sums
159(4)
Orthonormal Bases
163(5)
Summary
168(5)
References
169(1)
Problems
170(3)
Analog Systems and Signal Spaces
173(100)
Analog Systems
174(3)
Operations on Analog Signals
174(1)
Extensions to the Analog World
174(1)
Cross-Correlation, Autocorrelation, and Convolution
175(1)
Miscellaneous Operations
176(1)
Convolution and Analog LTI Systems
177(14)
Linearity and Translation-Invariance
177(2)
LTI Systems, Impulse Response, and Convolution
179(5)
Convolution Properties
184(2)
Dirac Delta Properties
186(2)
Splines
188(3)
Analog Signal Spaces
191(34)
lp Spaces
191(14)
Inner Product and Hilbert Spaces
205(6)
Orthonormal Bases
211(5)
Frames
216(9)
Modern Integration Theory
225(16)
Measure Theory
226(6)
Lebesgue Integration
232(9)
Distributions
241(18)
From Function to Functional
241(1)
From Functional to Distribution
242(5)
The Dirac Delta
247(3)
Distributions and Convolution
250(2)
Distributions as a Limit of a Sequence
252(7)
Summary
259(14)
Historical Notes
260(1)
Looking Forward
260(1)
Guide to Problems
260(1)
References
261(2)
Problems
263(10)
Time-Domain Signal Analysis
273(110)
Segmentation
277(11)
Basic Concepts
278(2)
Examples
280(3)
Classification
283(3)
Region Merging and Splitting
286(2)
Thresholding
288(12)
Global Methods
289(1)
Histograms
289(3)
Optimal Thresholding
292(7)
Local Thresholding
299(1)
Texture
300(14)
Statistical Measures
301(7)
Spectral Methods
308(6)
Structural Approaches
314(1)
Filtering and Enhancement
314(12)
Convolutional Smoothing
314(2)
Optimal Filtering
316(5)
Nonlinear Filters
321(5)
Edge Detection
326(12)
Edge Detection on a Simple Step Edge
328(4)
Signal Derivatives and Edges
332(2)
Conditions for Optimality
334(3)
Retrospective
337(1)
Pattern Detection
338(13)
Signal Correlation
338(4)
Structural Pattern Recognition
342(4)
Statistical Pattern Recognition
346(5)
Scale Space
351(18)
Signal Shape, Concavity, and Scale
354(3)
Gaussian Smoothing
357(12)
Summary
369(14)
References
369(6)
Problems
375(8)
Fourier Transforms of Analog Signals
383(57)
Fourier Series
385(18)
Exponential Fourier Series
387(4)
Fourier Series Convergence
391(6)
Trigonometric Fourier Series
397(6)
Fourier Transform
403(21)
Motivation and Definition
403(5)
Inverse Fourier Transform
408(3)
Properties
411(9)
Symmetry Properties
420(4)
Extension to L2(R)
424(8)
Fourier Transforms in L1(R) ∩ L2(R)
425(2)
Definition
427(2)
Isometry
429(3)
Summary
432(8)
Historical Notes
432(1)
Looking Forward
433(1)
References
433(1)
Problems
434(6)
Generalized Fourier Transforms of Analog Signals
440(42)
Distribution Theory and Fourier Transforms
440(11)
Examples
442(1)
The Generalized Inverse Fourier Transform
443(1)
Generalized Transform Properties
444(7)
Generalized Functions and Fourier Series Coefficients
451(8)
Dirac Comb: A Fourier Series Expansion
452(2)
Evaluating the Fourier Coefficients: Examples
454(5)
Linear Systems in the Frequency Domain
459(3)
Convolution Theorem
460(1)
Modulation Theorem
461(1)
Introduction to Filters
462(6)
Ideal Low-pass Filter
465(1)
Ideal High-pass Filter
465(1)
Ideal Bandpass Filter
465(3)
Modulation
468(7)
Frequency Translation and Amplitude Modulation
469(1)
Baseband Signal Recovery
470(1)
Angle Modulation
471(4)
Summary
475(7)
References
476(1)
Problems
477(5)
Discrete Fourier Transforms
482(72)
Discrete Fourier Transform
483(27)
Introduction
484(11)
The DFT's Analog Frequency-Domain Roots
495(2)
Properties
497(4)
Fast Fourier Transform
501(9)
Discrete-Time Fourier Transform
510(28)
Introduction
510(19)
Properties
529(5)
LTI Systems and the DTFT
534(4)
The Sampling Theorem
538(9)
Band-Limited Signals
538(2)
Recovering Analog Signals from Their Samples
540(3)
Reconstruction
543(2)
Uncertainty Principle
545(2)
Summary
547(7)
References
548(1)
Problems
549(5)
The z-Transform
554(31)
Conceptual Foundations
555(11)
Definition and Basic Examples
555(2)
Existence
557(4)
Properties
561(5)
Inversion Methods
566(7)
Contour Integration
566(1)
Direct Laurent Series Computation
567(2)
Properties and z-Transform Table Lookup
569(2)
Application: Systems Governed by Difference Equations
571(2)
Related Transforms
573(4)
Chirp z-Transform
573(2)
Zak Transform
575(2)
Summary
577(8)
Historical Notes
578(1)
Guide to Problems
578(1)
References
578(2)
Problems
580(5)
Frequency-Domain Signal Analysis
585(127)
Narrowband Signal Analysis
586(22)
Single Oscillatory Component: Sinusoidal Signals
587(1)
Application: Digital Telephony DTMF
588(16)
Filter Frequency Response
604(1)
Delay
605(3)
Frequency and Phase Estimation
608(12)
Windowing
609(2)
Windowing Methods
611(2)
Power Spectrum Estimation
613(5)
Application: Interferometry
618(2)
Discrete filter design and implementation
620(23)
Ideal Filters
621(2)
Design Using Window Functions
623(1)
Approximation
624(2)
Z-Transform Design Techniques
626(6)
Low-Pass Filter Design
632(7)
Frequency Transformations
639(1)
Linear Phase
640(3)
Wideband Signal Analysis
643(7)
Chirp Detection
643(3)
Speech Analysis
646(4)
Problematic Examples
650(1)
Analog Filters
650(36)
Introduction
651(1)
Basic Low-Pass Filters
652(2)
Butterworth
654(10)
Chebyshev
664(6)
Inverse Chebyshev
670(6)
Elliptic Filters
676(9)
Application: Optimal Filters
685(1)
Specialized Frequency-Domain Techniques
686(14)
Chirp-z Transform Application
687(1)
Hilbert Transform
688(6)
Perfect Reconstruction Filter Banks
694(6)
Summary
700(12)
References
701(3)
Problems
704(8)
Time-Frequency Signal Transforms
712(90)
Gabor Transforms
713(23)
Introduction
715(2)
Interpretations
717(1)
Gabor Elementary Functions
718(5)
Inversion
723(7)
Applications
730(5)
Properties
735(1)
Short-Time Fourier Transforms
736(11)
Window Functions
736(2)
Transforming with a General Window
738(2)
Properties
740(1)
Time-Frequency Localization
741(6)
Discretization
747(13)
Transforming Discrete Signals
747(2)
Sampling the Short-Time Fourier Transform
749(2)
Extracting Signal Structure
751(3)
A Fundamental Limitation
754(3)
Frames of Windowed Fourier Atoms
757(2)
Status of Gabor's Problem
759(1)
Quadratic Time-Frequency Transforms
760(11)
Spectrogram
761(1)
Wigner--Ville Distribution
761(8)
Ambiguity Function
769(1)
Cross-Term Problems
769(1)
Kernel Construction Method
770(1)
The Balian--Low Theorem
771(16)
Orthonormal Basis Decomposition
772(5)
Frame Decomposition
777(10)
Avoiding the Balian--Low Trap
787(1)
Summary
787(15)
Historical Notes
789(1)
Resources
790(1)
Looking Forward
791(1)
References
791(3)
Problems
794(8)
Time-Scale Signal Transforms
802(71)
Signal Scale
803(1)
Continuous Wavelet Transforms
803(18)
An Unlikely Discovery
804(1)
Basic Theory
804(11)
Examples
815(6)
Frames
821(11)
Discretization
822(2)
Conditions on Wavelet Frames
824(1)
Constructing Wavelet Frames
825(4)
Better Localization
829(3)
Multiresolution Analysis and Orthogonal Wavelets
832(31)
Multiresolution Analysis
835(12)
Scaling Function
847(5)
Discrete Low-Pass Filter
852(5)
Orthonormal Wavelet
857(6)
Summary
863(10)
References
865(2)
Problems
867(6)
Mixed-Domain Signal Analysis
873(56)
Wavelet Methods for Signal Structure
873(20)
Discrete Wavelet Transform
874(1)
Wavelet Pyramid Decomposition
875(8)
Application: Multiresolution Shape Recognition
883(10)
Mixed-Domain Signal Processing
893(7)
Filtering Methods
895(2)
Enhancement Techniques
897(3)
Biophysical Applications
900(4)
David Marr's Program
900(1)
Psychophysics
900(4)
Discovering Signal Structure
904(9)
Edge Detection
905(3)
Local Frequency Detection
908(4)
Texture Analysis
912(1)
Pattern Recognition Networks
913(4)
Coarse-to-Fine Methods
913(2)
Pattern Recognition Networks
915(1)
Neural Networks
916(1)
Application: Process Control
916(1)
Signal Modeling and Matching
917(1)
Hidden Markov Models
917(1)
Matching Pursuit
918(1)
Applications
918(1)
Afterword
918(11)
References
919(6)
Problems
925(4)
Index 929


RONALD L. ALLEN received his BA in mathematics from the University of California, Berkeley in 1973, his MA in mathematics from the University of California, Los Angeles in 1975, and his MS and PhD in Computer Science from the University of Texas at Arlington in 1990 and 1993, respectively. DUNCAN W. MILLS received his BA in Physics from Wesleyan University, his MS in Electrical Engineering from George Washington University, and his PhD in Electrical Engineering from University of Texas at Dallas in 1992.