Statistical signal processing in engineering

A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast t...

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Detalles Bibliográficos
Otros Autores:	Spagnolini, Umberto, author (author)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Hoboken, New Jersey : Wiley 2018.
Edición:	1st edition
Materias:	Signal processing > Statistical methods.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009631502906719

Tabla de Contenidos:

Intro
Title Page
Copyright Page
Contents
List of Figures
List of Tables
Preface
List of Abbreviations
How to Use the Book
About the Companion Website
Prerequisites
Why are there so many matrixes in this book?
Chapter 1 Manipulations on Matrixes
1.1 Matrix Properties
1.1.1 Elementary Operations
1.2 Eigen-Decompositions
1.3 Eigenvectors in Everyday Life
1.3.1 Conversations in a Noisy Restaurant
1.3.2 Power Control in a Cellular Communication System
1.3.3 Price Equilibrium in the Economy
1.4 Derivative Rules
1.4.1 Derivative with respect to x∈ Rn
1.4.2 Derivative with respect to x∈ Cn
1.4.3 Derivative with respect to the Matrix X∈Rm×n
1.5 Quadratic Forms
1.6 Diagonalization of a Quadratic Form
1.7 Rayleigh Quotient
1.8 Basics of Optimization
1.8.1 Quadratic Function with Simple Linear Constraint (M=1)
1.8.2 Quadratic Function with Multiple Linear Constraints
Appendix A: Arithmetic vs. Geometric Mean
Chapter 2 Linear Algebraic Systems
2.1 Problem Definition and Vector Spaces
2.1.1 Vector Spaces in Tomographic Radiometric Inversion
2.2 Rotations
2.3 Projection Matrixes and Data-Filtering
2.3.1 Projections and Commercial FM Radio
2.4 Singular Value Decomposition (SVD) and Subspaces
2.4.1 How to Choose the Rank of A?
2.5 QR and Cholesky Factorization
2.6 Power Method for Leading Eigenvectors
2.7 Least Squares Solution of Overdetermined Linear Equations
2.8 Efficient Implementation of the LS Solution
2.9 Iterative Methods
Chapter 3 Random Variables in Brief
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties
3.2 Convexity and Jensen Inequality
3.3 Uncorrelatedness and Statistical Independence
3.4 Real-Valued Gaussian Random Variables.
3.5 Conditional pdf for Real-Valued Gaussian Random Variables
3.6 Conditional pdf in Additive Noise Model
3.7 Complex Gaussian Random Variables
3.7.1 Single Complex Gaussian Random Variable
3.7.2 Circular Complex Gaussian Random Variable
3.7.3 Multivariate Complex Gaussian Random Variables
3.8 Sum of Square of Gaussians: Chi-Square
3.9 Order Statistics for N rvs
Chapter 4 Random Processes and Linear Systems
4.1 Moment Characterizations and Stationarity
4.2 Random Processes and Linear Systems
4.3 Complex-Valued Random Processes
4.4 Pole-Zero and Rational Spectra (Discrete-Time)
4.4.1 Stability of LTI Systems
4.4.2 Rational PSD
4.4.3 Paley-Wiener Theorem
4.5 Gaussian Random Process (Discrete-Time)
4.6 Measuring Moments in Stochastic Processes
Appendix A: Transforms for Continuous-Time Signals
Appendix B: Transforms for Discrete-Time Signals
Chapter 5 Models and Applications
5.1 Linear Regression Model
5.2 Linear Filtering Model
5.2.1 Block-Wise Circular Convolution
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes
5.2.3 Identification and Deconvolution
5.3 MIMO systems and Interference Models
5.3.1 DSL System
5.3.2 MIMO in Wireless Communication
5.4 Sinusoidal Signal
5.5 Irregular Sampling and Interpolation
5.5.1 Sampling With Jitter
5.6 Wavefield Sensing System
Chapter 6 Estimation Theory
6.1 Historical Notes
6.2 Non-Bayesian vs. Bayesian
6.3 Performance Metrics and Bounds
6.3.1 Bias
6.3.2 Mean Square Error (MSE)
6.3.3 Performance Bounds
6.4 Statistics and Sufficient Statistics
6.5 MVU and BLU Estimators
6.6 BLUE for Linear Models
6.7 Example: BLUE of the Mean Value of Gaussian rvs
Chapter 7 Parameter Estimation
7.1 Maximum Likelihood Estimation (MLE)
7.2 MLE for Gaussian Model xN(μ(θ),C(θ)).
7.2.1 Additive Noise Model x=s(θ)+w with wN(0,Cw)
7.2.2 Additive Noise Model x=H(ω)·α+w with wN(0,Cw)
7.2.3 Additive Noise Model with Multiple Observations x=s(θ)+w with wN(0,Cw), Cw Known
7.2.3.1 Linear Model = ⋅ +
7.2.3.2 Model = ⋅ +
7.2.3.3 Model = ( ) ⋅ +
7.2.4 Model xN(0,C(θ))
7.2.5 Additive Noise Model with Multiple Observations x=s(θ)+w with wN(0,Cw), Cw Unknown
7.3 Other Noise Models
7.4 MLE and Nuisance Parameters
7.5 MLE for Continuous-Time Signals
7.5.1 Example: Amplitude Estimation
7.5.2 MLE for Correlated Noise Sw(f)
7.6 MLE for Circular Complex Gaussian
7.7 Estimation in Phase/Frequency Modulations
7.7.1 MLE Phase Estimation
7.7.2 Phase Locked Loops
7.8 Least Squares (LS) Estimation
7.8.1 Weighted LS with W = diag{c1,c2,...,cN}
7.8.2 LS Estimation and Linear Models
7.8.3 Under or Over-Parameterizing?
7.8.4 Constrained LS Estimation
7.9 Robust Estimation
Chapter 8 Cramér-Rao Bound
8.1 Cramér-Rao Bound and Fisher Information Matrix
8.1.1 CRB for Scalar Problem (P=1)
8.1.2 CRB and Local Curvature of Log-Likelihood
8.1.3 CRB for Multiple Parameters (p≥1)
8.2 Interpretation of CRB and Remarks
8.2.1 Variance of Each Parameter
8.2.2 Compactness of the Estimates
8.2.3 FIM for Known Parameters
8.2.4 Approximation of the Inverse of FIM
8.2.5 Estimation Decoupled From FIM
8.2.6 CRB and Nuisance Parameters
8.2.7 CRB for Non-Gaussian rv and Gaussian Bound
8.3 CRB and Variable Transformations
8.4 FIM for Gaussian Parametric Model xN(μ(θ),C(θ))
8.4.1 FIM for x=s(θ)+w with wN(0,Cw)
8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise
8.4.3 FIM for Circular Complex Model
Appendix A: Proof of CRB
Appendix B: FIM for GaussianModel
Appendix C: Some Derivatives for MLE and CRB Computations.
Chapter 9 MLE and CRB for Some Selected Cases
9.1 Linear Regressions
9.2 Frequency Estimation x[n]=aocos(ω0n+ϕo)+w[n]
9.3 Estimation of Complex Sinusoid
9.3.1 Proper, Improper, and Non-Circular Signals
9.4 Time of Delay Estimation
9.5 Estimation of Max for Uniform pdf
9.6 Estimation of Occurrence Probability for Binary pdf
9.7 How to Optimize Histograms?
9.8 Logistic Regression
Chapter 10 Numerical Analysis and Montecarlo Simulations
10.1 System Identification and Channel Estimation
10.1.1 Matlab Code and Results
10.2 Frequency Estimation
10.2.1 Variable (Coarse/Fine) Sampling
10.2.2 Local Parabolic Regression
10.2.3 Matlab Code and Results
10.3 Time of Delay Estimation
10.3.1 Granularity of Sampling in ToD Estimation
10.3.2 Matlab Code and Results
10.4 Doppler-Radar System by Frequency Estimation
10.4.1 EM Method
10.4.2 Matlab Code and Results
Chapter 11 Bayesian Estimation
11.1 Additive Linear Model with Gaussian Noise
11.1.1 Gaussian A-priori: θN(,σθ2)
11.1.2 Non-Gaussian A-Priori
11.1.3 Binary Signals: MMSE vs. MAP Estimators
11.1.4 Example: Impulse Noise Mitigation
11.2 Bayesian Estimation in Gaussian Settings
11.2.1 MMSE Estimator
11.2.2 MMSE Estimator for Linear Models
11.3 LMMSE Estimation and Orthogonality
11.4 Bayesian CRB
11.5 Mixing Bayesian and Non-Bayesian
11.5.1 Linear Model with Mixed Random/Deterministic Parameters
11.5.2 Hybrid CRB
11.6 Expectation-Maximization (EM)
11.6.1 EM of the Sum of Signals in Gaussian Noise
11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms
11.6.3 Remarks
Chapter 12 Optimal Filtering
12.1 Wiener Filter
12.2 MMSE Deconvolution (or Equalization)
12.3 Linear Prediction
12.3.1 Yule-Walker Equations
12.4 LS Linear Prediction.
12.5 Linear Prediction and AR Processes
12.6 Levinson Recursion and Lattice Predictors
Chapter 13 Bayesian Tracking and Kalman Filter
13.1 Bayesian Tracking of State in Dynamic Systems
13.1.1 Evolution of the A-Posteriori pdf
13.2 Kalman Filter (KF)
13.2.1 KF Equations
13.2.2 Remarks
13.3 Identification of Time-Varying Filters in Wireless Communication
13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems
13.5 Position Tracking by Multi-Lateration
13.5.1 Positioning and Noise
13.5.2 Example of Position Tracking
13.6 Non-Gaussian Pdf and Particle Filters
Chapter 14 Spectral Analysis
14.1 Periodogram
14.1.1 Bias of the Periodogram
14.1.2 Variance of the Periodogram
14.1.3 Filterbank Interpretation
14.1.4 Pdf of the Periodogram (White Gaussian Process)
14.1.5 Bias and Resolution
14.1.6 Variance Reduction and WOSA
14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid
14.2 Parametric Spectral Analysis
14.2.1 MLE and CRB
14.2.2 General Model for AR, MA, ARMA Spectral Analysis
14.3 AR Spectral Analysis
14.3.1 MLE and CRB
14.3.2 A Good Reason to Avoid Over-Parametrization in AR
14.3.3 Cramér-Rao Bound of Poles in AR Spectral Analysis
14.3.4 Example: Frequency Estimation by AR Spectral Analysis
14.4 MA Spectral Analysis
14.5 ARMA Spectral Analysis
14.5.1 Cramér-Rao Bound for ARMA Spectral Analysis
Appendix A:Which Sample Estimate of the Autocorrelation to Use?
Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix
Appendix C: Property of Monic Polynomial
Appendix D: Variance of Pole in AR(1)
Chapter 15 Adaptive Filtering
15.1 Adaptive Interference Cancellation
15.2 Adaptive Equalization in Communication Systems
15.2.1 Wireless Communication Systems in Brief
15.2.2 Adaptive Equalization.
15.3 Steepest Descent MSE Minimization.

Statistical signal processing in engineering

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