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E-raamat: Analog and Digital Signal Analysis: From Basics to Applications

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Analog and Digital Signal Analysis: From Basics to ApplicationsSuurem pilt
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This book provides comprehensive, graduate-level treatment of analog and digital signal analysis suitable for course use and self-guided learning. This expert text guides the reader from the basics of signal theory through a range of application tools for use in acoustic analysis, geophysics, and data compression. Each concept is introduced and explained step by step, and the necessary mathematical formulae are integrated in an accessible and intuitive way. The first part of the book explores how analog systems and signals form the basics of signal analysis. This section covers Fourier series and integral transforms of analog signals, Laplace and Hilbert transforms, the main analog filter classes, and signal modulations. Part II covers digital signals, demonstrating their key advantages. It presents z and Fourier transforms, digital filtering, inverse filters, deconvolution, and parametric modeling for deterministic signals. Wavelet decomposition and reconstruction of non-stationary signals are also discussed. The third part of the book is devoted to random signals, including spectral estimation, parametric modeling, and Tikhonov regularization. It covers statistics of one and two random variables and the principles and methods of spectral analysis. Estimation of signal properties is discussed in the context of ergodicity conditions and parameter estimations, including the use of Wiener and Kalman filters. Two appendices cover the basics of integration in the complex plane and linear algebra. A third appendix presents a basic Matlab toolkit for computer signal analysis. This expert text provides both a solid theoretical understanding and tools for real-world applications.

Arvustused

The first thing to say about this book is that it is comprehensive. Its 600+ pages cover a lot of ground and at a fairly deep level. Overall impressions are positive and the book is definitely a valuable addition to my library. (Todd Welti, Journal of the Audio Engineering Society, Vol. 65 (5), May, 2017)  

1 Notions on Systems
1(10)
1.1 Linear Systems
1(1)
1.2 Stationary Systems
2(1)
1.3 Continuous Systems
3(1)
1.4 Linear Time Invariant Systems (LTI)
3(4)
1.4.1 Eigenfunctions of LTI Systems
3(3)
1.4.2 Transfer Function and Frequency Response
6(1)
1.5 Linear Differential Equations with Constant Coefficients
7(1)
1.6 Linearity of Physical Systems
8(3)
2 First and Second Order Systems
11(24)
2.1 First Order System. R, C Circuit
11(10)
2.1.1 Transfer Function
12(1)
2.1.2 Frequency Response
13(2)
2.1.3 Graphic Representation of the Frequency Response
15(2)
2.1.4 Geometric Interpretation of the Variation of the Frequency Response
17(2)
2.1.5 R, C Circuit with Output on the Resistor Terminals
19(2)
2.2 Second Order System. R, L, C Series Circuit
21(8)
2.2.1 Transfer Function
21(2)
2.2.2 Second Order System Frequency Response
23(1)
2.2.3 Geometric Interpretation of the Variation of the Frequency Response
23(5)
2.2.4 Bode Representation of the Gain
28(1)
2.3 Case of Sharp Resonance
29(1)
2.4 Quality Factor Q
30(5)
3 Fourier Series
35(24)
3.1 Decomposition of a Periodic Function in Fourier Series
37(5)
3.2 Parseval's Theorem for Fourier Series
42(3)
3.3 Sum of a Finite Number of Exponentials
45(3)
3.4 Hilbert Spaces
48(3)
3.5 Gibbs Phenomenon
51(2)
3.6 Nonlinearity of a System and Harmonic Generation
53(6)
4 The Dirac Distribution
59(18)
4.1 Infinite Sum of Exponentials. Cauchy Principal Value
60(1)
4.2 Dirichlet Integral
61(6)
4.3 Dirac Distribution
67(10)
4.3.1 Definition
67(2)
4.3.2 Properties of the Dirac Distribution
69(1)
4.3.3 Definition of the Convolution Product
70(2)
4.3.4 Primitive of the Dirac Distribution. Heaviside Function
72(1)
4.3.5 Derivatives of the Dirac Distribution
73(4)
5 Fourier Transform
77(16)
5.1 Impulse Response of an LTI System
77(2)
5.2 Fourier Transform of a Signal
79(3)
5.2.1 Direct Fourier Transform
79(1)
5.2.2 Inverse Fourier Transform
79(3)
5.3 Properties of Fourier Transform
82(2)
5.3.1 Symmetry Properties of the Fourier Transform of a Real Signal
82(1)
5.3.2 Time-Delay Property of the Fourier Transform
83(1)
5.4 Power and Energy of a Signal; Parseval--Plancherel Theorem
84(2)
5.5 Deriving a Signal and Fourier Transform
86(1)
5.6 Fourier Transform of Dirac Distribution and of Trigonometric Functions
87(2)
5.7 Two-Dimensional Fourier Transform
89(4)
6 Fourier Transform and LTI Filter Systems
93(18)
6.1 Response of a LTI System to Any Form of Input Signal
93(2)
6.2 Temporal Relastionship Between the Input and Output Signals of an LTI Filter
95(1)
6.3 Fourier Transform and Convolution in Physics
96(1)
6.4 Fourier Transform of the Product of Two Functions
97(1)
6.5 Fourier Transform of a Periodic Function
98(1)
6.6 Deterministic Correlation Functions
99(3)
6.7 Signal Spreads. Heisenberg-Gabor Uncertainty Relationship
102(9)
7 Fourier Transforms and Convolution Calculations
111(26)
7.1 Fourier Transformation of Common Fonctions
111(9)
7.1.1 Fourier Transform of a Rectangular Window
111(2)
7.1.2 Fourier Transform of a Triangular Window
113(1)
7.1.3 Fourier Transform of Hanning Window
114(1)
7.1.4 Fourier Transform of a Gaussian Function
115(5)
7.2 Behavior at Infinity of the Fourier Amplitude of a Signal
120(1)
7.3 Limitation in Time or Frequency of a Signal
120(4)
7.3.1 Fourier Transform of a Time-Limited Cosine
120(2)
7.3.2 Practical Interest of Multiplying a Signal by a Time Window Before Calculating a Spectrum
122(1)
7.3.3 Frequency Limitation; Gibbs Phenomenon
122(2)
7.4 Convolution Calculations
124(13)
7.4.1 Response of a First Order System to Different Input Signals
124(4)
7.4.2 Examples of Calculations of Convolution
128(9)
8 Impulse Response of LTI Systems
137(12)
8.1 Impulse Response of a First-Order Filter
138(4)
8.2 Impulse Response of a Second Order Filter
142(7)
9 Laplace Transform
149(10)
9.1 Direct and Inverse Transforms
149(4)
9.1.1 Study of Convergence with an Example
151(2)
9.1.2 Another Example
153(1)
9.2 Stability of a System and Laplace Transform
153(2)
9.2.1 Marginal Stability
154(1)
9.2.2 Minimum-Phase Filter
155(1)
9.3 Applications of Laplace Transform
155(4)
9.3.1 Response of a System to Any Input Signal
157(2)
10 Analog Filters
159(18)
10.1 Delay of a Signal Crossing a Low-Pass Filter
159(2)
10.2 Butterworth Filters
161(5)
10.3 Chebyshev Filters
166(2)
10.4 Bessel Filters
168(2)
10.5 Comparison of the Different Filters Responses
170(7)
11 Causal Signals---Analytic Signals
177(30)
11.1 Fourier Transform of the Pseudo-Function 1/t
177(4)
11.2 Fourier Transform of a Causal Signal; Hilbert Transform
181(4)
11.3 Paley-Wiener Theorem
185(1)
11.4 Analytic Signal
186(11)
11.4.1 Instantaneous Frequency of a Chirp
190(1)
11.4.2 Double-Sideband (DSB) Signal Modulation
190(3)
11.4.3 Single-Sideband Signal Modulation (SSB)
193(2)
11.4.4 Band-pass Filtering of Amplitude Modulated Signal
195(2)
11.5 Phase and Group Time Delays
197(2)
11.6 Decomposition of a Voice Signal by a Filter Bank
199(8)
12 Time--Frequency Analysis
207(20)
12.1 Short-Time Fourier Transform (STFT) and Spectrogram
208(4)
12.2 Wigner--Ville Distribution
212(5)
12.3 Continuous Wavelet Transform
217(10)
12.3.1 Examples of Wavelets
217(2)
12.3.2 Decomposition and Reconstruction of a Signal with Wavelets
219(5)
12.3.3 Shannon Wavelet
224(3)
13 Notions on Digital Signals
227(8)
13.1 Analog to Digital Conversion
228(2)
13.2 Criterion for a Good Sampling in Time Domain
230(2)
13.3 Simple Digital Signals
232(3)
14 Discrete Systems---Moving Average Systems
235(18)
14.1 Linear, Time-Invariant Systems (LTI)
236(1)
14.2 Properties of LTI Systems
236(1)
14.3 Notion of Transfer Function
237(2)
14.4 Frequency Response of a LTI System
239(1)
14.5 Moving Average (MA) Filters
240(1)
14.6 Geometric Interpretation of Gain Variation with Frequency
241(3)
14.7 Properties of Moving Average (MA) Filters, also Called Finite Impulse Response (FTR)
244(2)
14.8 Other Examples of All-Zero Filters (MA)
246(7)
15 Z-Transform
253(10)
15.1 Definition
253(3)
15.2 Inversion of z-Transform
256(2)
15.3 z-Transform of the Product of Two Functions
258(1)
15.4 Properties of the z-Transform
259(1)
15.5 Applications
259(4)
16 Fourier Transform of Digital Signals
263(28)
16.1 Poisson's Summation Formula
264(1)
16.2 Shannon Aliasing Theorem
265(2)
16.3 Sampling Theorem of Shannon--Whittaker
267(2)
16.4 Application of Poisson's Summation Formula: Fourier Transform of a Sine
269(1)
16.5 Fourier Transform of a Product of Functions of Time
270(1)
16.6 Parseval's Theorem
271(1)
16.7 Fourier Transform of a Rectangular Window
272(1)
16.8 Fourier Transform of a Sine Function Limited in Time
273(2)
16.9 Apodization Windows
275(4)
16.10 Discrete Fourier Transform (DFT)
279(2)
16.10.1 Important Special Case: The DFT of a Bounded Support Function
281(1)
16.11 Fast Fourier Transform Algorithm (FFT)
281(3)
16.12 Matrix Form of DFT
284(1)
16.13 Signal Interpolation by Zero Padding
284(2)
16.14 Artifacts of the Fourier Transform on a Computer
286(5)
17 Autoregressive Systems (AR)---ARMA Systems
291(30)
17.1 Autoregressive First-Order System
292(5)
17.1.1 Case of a Causal System
292(3)
17.1.2 Analysis of the Anticausal System
295(2)
17.2 Autoregressive System (Recursive) of Second Order
297(8)
17.2.1 Calculation of the System Transfer Function H(z)
297(2)
17.2.2 Geometric Interpretation of Variation of Frequency Gain Magnitude
299(3)
17.2.3 Impulse Response of Second-Order System
302(1)
17.2.4 Functional Diagrams of the Digital System of Second Order
303(2)
17.3 ARMA Filters
305(5)
17.4 Transition from an Analog Filter to a Digital Filter
310(11)
17.4.1 Correspondence by the Bilinear Transformation
310(2)
17.4.2 Correspondence by Impulse Response Sampling
312(1)
17.4.3 Correspondence by Frequency Response Sampling
313(8)
18 Minimum-Phase Systems---Deconvolution
321(16)
18.1 Minimum-Phase Systems
321(6)
18.1.1 Notion of Minimum-Phase System
321(5)
18.1.2 Properties of Minimum-Phase Systems
326(1)
18.2 Deconvolution
327(10)
18.2.1 Interest of Deconvolution
327(1)
18.2.2 Deconvolution Techniques
328(9)
19 Wavelets; Multiresolution Analysis
337(38)
19.1 Dyadic Decomposition-Reconstruction of a Digital Signal; Two Channels Filter Bank
338(8)
19.2 Multiresolution Wavelet Analysis
346(7)
19.3 Daubechies Wavelets
353(22)
20 Parametric Estimate---Modeling of Deterministic Signals---Linear Prediction
375(32)
20.1 Least Square Method
376(2)
20.2 Pade Representation
378(7)
20.2.1 Pade Approximation
381(1)
20.2.2 All-pole Modeling
381(1)
20.2.3 Examples
382(3)
20.3 Prony's Approximation Method. Shanks Method
385(7)
20.3.1 Prony's Method
385(4)
20.3.2 Shanks Method
389(3)
20.4 All-pole Modeling in the Context of the Prony's Method
392(2)
20.5 All-pole Modeling in the Case of a Finite Number of Data
394(2)
20.5.1 Autocorrelation Method
394(1)
20.5.2 Covariance Method
395(1)
20.6 Adaptive Filter
396(11)
References
405(2)
21 Random Signals: Statistics Basis
407(38)
21.1 First-Order Statistics
408(13)
21.1.1 Case of a Real Random Variable
408(5)
21.1.2 Gaussian Distribution (Normal Law)
413(6)
21.1.3 Probability Density Function of a Function of a Random Variable
419(2)
21.2 Second-Order Statistics
421(24)
21.2.1 Case of Two Real Random Variables
421(7)
21.2.2 Two Joint Gaussian r.r.
428(3)
21.2.3 Properties of the Sum of Two r.v.
431(4)
21.2.4 Complex Random Variables
435(10)
22 Multiple Random Variables---Linear Regression Maximum Likelihood Estimation
445(22)
22.1 Χ2υ (Chi-Square) Variable with υ Degrees of Freedom
445(4)
22.2 Least Squares Linear Regression
449(3)
22.2.1 Simple Method
449(2)
22.2.2 Elaborate Method
451(1)
22.3 Linear Regression with Noise on Data---Tikhonov Regularization
452(3)
22.4 Parametric Estimation
455(12)
22.4.1 Issues of the Estimation
455(3)
22.4.2 Maximum Likelihood Parametric Estimation
458(2)
22.4.3 Cramer-Rao Bound
460(7)
23 Correlation and Covariance Matrices of a Complex Random Vector
467(16)
23.1 Definition of Correlation and Covariance Matrices
467(2)
23.1.1 Properties of Correlation Matrix
468(1)
23.2 Linear Transformation of Random Vectors
469(2)
23.3 Multivariate Gaussian Probability Density Functions
471(3)
23.4 Estimation of the Correlation Matrix from Observations
474(2)
23.5 Karhunen-Loeve Development
476(7)
23.5.1 Example of Using the Correlation and Covariance Matrices
476(2)
23.5.2 Theoretical Aspects
478(2)
23.5.3 Optimality of Karhunen-Loeve Development
480(3)
24 Correlation Functions, Spectral Power Densities of Random Signals
483(28)
24.1 Correlation Function of a Random Signal
483(3)
24.1.1 Correlation Function of a Wide Sense Stationary (WSS) Signal
484(1)
24.1.2 Properties of the Correlation Function
485(1)
24.1.3 Centered White Noise
486(1)
24.2 Filtering a Random Signal by a LTI Filter
486(2)
24.2.1 Expected Values
486(1)
24.2.2 Correlation Functions of Input and Output Signals
487(1)
24.3 Power Spectral Density of a WSS Signal
488(3)
24.4 Filtering a Centered White Noise with a First Order Filter
491(2)
24.5 Coherence Function
493(3)
24.6 Autocorrelation Matrix of a Random Signal
496(1)
24.7 Beamforming
497(1)
24.8 Analog Random Signals
498(3)
24.9 Matched Filter
501(10)
25 Ergodicity; Temporal and Spectral Estimations
511(18)
25.1 Estimation of the Average of a Random Signal
512(3)
25.1.1 Expectation of the Average Estimator
512(1)
25.1.2 Variance of the Average Estimator
512(2)
25.1.3 Ergodicity Conditions
514(1)
25.2 Estimation of the Correlation Function
515(2)
25.3 Spectral Estimation
517(5)
25.3.1 Raw Estimator of the Power Spectral Density or Periodogram
518(1)
25.3.2 Statistical Properties of the Periodogram
519(3)
25.4 Improvement of the Spectral Estimation
522(2)
25.5 Search for Harmonic Components
524(5)
25.5.1 Capon Method ("Maximum Likelihood")
524(2)
25.5.2 Pisarenko Method
526(3)
26 Parametric Modeling of Random Signals
529(14)
26.1 Paley--Wiener Condition
529(3)
26.2 Parametric Modeling of Random Signals
532(11)
26.2.1 Yule-Walker Equations
532(3)
26.2.2 Search of the ARMA Model Coefficients for a Regular Process
535(1)
26.2.3 AR Modeling of a Regular Random Signal
536(2)
26.2.4 MA Modeling of a Regular Random Signal
538(5)
27 Optimal Filtering; Wiener and Kalman Filters
543(20)
27.1 Optimal Estimation
544(1)
27.1.1 Stochastic Orthogonality
544(1)
27.1.2 Optimal Least Squares Estimate
544(1)
27.2 Wiener Optimal Filtering
545(7)
27.2.1 FTR Wiener Filter
545(4)
27.2.2 Linear Prediction of a Random Signal
549(3)
27.3 IIR Wiener Filter
552(3)
27.3.1 Non-Causal Filter
552(1)
27.3.2 Causal Filter
553(2)
27.4 Kalman Filter
555(8)
27.4.1 Recursive Estimate of a Constant State
555(1)
27.4.2 General Form of the Kalman Recursive Equation
556(7)
Appendix A Functions of a Complex Variable 563(10)
Appendix B Linear Algebra 573(18)
Appendix C Computer Calculations 591(10)
Bibliography 601(4)
Index 605
Frédéric Cohen Tenoudji is Emeritus Professor at Pierre and Marie Curie University in Paris. His research field is non-destructive evaluation by ultrasonics, defect characterization, and linear and non-linear sound propagation in heterogeneous materials with applications to civil engineering: concrete cure monitoring, materials structural integrity. He develops ultrasound instrumentation for NDE with graphic user interface and embedded signal processing. Cohen Tenoudji teaches signal processing, sensors, ultrasonics, and object-oriented programming. From 1985-86 he was Member of the Technical Staff at the Science Center of Rockwell International, NDE department, in Thousand Oaks, California.
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