Spagnolini U. Statistical Signal Processing in Engineering

Wiley, 2018. — 608 p. — ISBN: 978-1119293972.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 theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.Manipulations on Matrixes
Matrix Properties.
Eigen-Decompositions.
Eigenvectors in Everyday Life.
Derivative Rules.
Quadratic Forms.
Diagonalization of a Quadratic Form.
Rayleigh Quotient.
Basics of Optimization.
Appendix: Arithmetic vs. Geometric Mean.Linear Algebraic Systems
Problem Definition and Vector Spaces.
Rotations.
Projection Matrixes and Data-Filtering.
Singular Value Decomposition (SVD) and Subspaces
QR and Cholesky Factorization.
Power Method for Leading Eigenvectors.
Least Squares Solution of Overdetermined Linear Equations.
Efficient Implementation of the LS Solution.
Iterative Methods.Random Variables in Brief
Probability Density Function (PDF), Moments, and Other Useful Properties.
Convexity and Jensen Inequality.
Uncorrelatedness and Statistical Independence.
Real-Valued Gaussian Random Variables.
Conditional PDF for Real-Valued Gaussian Random Variables.
Conditional PDF in Additive Noise Model.
Complex Gaussian Random Variables.
Sum of Square of Gaussians: Chi-Square.
Order Statistics for N rvs.Random Processes and Linear Systems
Moment Characterizations and Stationarity.
Random Processes and Linear Systems.
Complex-Valued Random Processes.
Pole-Zero and Rational Spectra (Discrete-Time).
Gaussian Random Process (Discrete-Time).
Measuring Moments in Stochastic Processes.
Appendix: Transforms for Continuous-Time Signals.
Appendix: Transforms for Discrete-Time Signals.Models and Applications
Linear Regression Model.
Linear Filtering Model.
MIMO systems and Interference Models.
Sinusoidal Signal.
Irregular Sampling and Interpolation.
Wavefield Sensing System.Estimation Theory
Historical Notes.
Non-Bayesian vs. Bayesian.
Performance Metrics and Bounds.
Statistics and Sufficient Statistics.
MVU and BLU Estimators.
BLUE for Linear Models.
Example: BLUE of the Mean Value of Gaussian rvs.Parameter Estimation
Maximum Likelihood Estimation (MLE).
MLE for Gaussian Model x ~ N(μ(θ),C(θ)).
Other Noise Models.
MLE and Nuisance Parameters.
MLE for Continuous-Time Signals.
MLE for Circular Complex Gaussian.
Estimation in Phase/Frequency Modulations.
Least Squares (LS) Estimation.
Robust Estimation.Cramér–Rao Bound
Cramér–Rao Bound and Fisher Information Matrix.
Interpretation of CRB and Remarks.
CRB and Variable Transformations.
FIM for Gaussian Parametric Model x ~ N(μ(θ),C(θ)).
Appendix: Proof of CRB.
Appendix: FIM for Gaussian Model.
Appendix: Some Derivatives for MLE and CRB Computations.MLE and CRB for Some Selected Cases
Linear Regressions.
Frequency Estimation x[n] = a₀cos(ω₀n + φ₀) + w[n].
Estimation of Complex Sinusoid.
Time of Delay Estimation.
Estimation of Max for Uniform PDF.
Estimation of Occurrence Probability for Binary PDF.
How to Optimize Histograms?
Logistic Regression.Numerical Analysis and Montecarlo Simulations
System Identification and Channel Estimation.
Frequency Estimation.
Time of Delay Estimation.
Doppler-Radar System by Frequency Estimation.Bayesian Estimation
Additive Linear Model with Gaussian Noise.
Bayesian Estimation in Gaussian Settings.
LMMSE Estimation and Orthogonality.
Bayesian CRB.
Mixing Bayesian and Non-Bayesian.
Expectation-Maximization (EM).
Appendix: Gaussian Mixture PDF.Optimal Filtering
Wiener Filter.
MMSE Deconvolution (or Equalization).
Linear Prediction.
LS Linear Prediction.
Linear Prediction and AR Processes.
Levinson Recursion and Lattice Predictors.Bayesian Tracking and Kalman Filter
Bayesian Tracking of State in Dynamic Systems.
Kalman Filter (KF).
Identification of Time-Varying Filters in Wireless Communication.
Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems.
Position Tracking by Multi-Lateration.
Non-Gaussian PDF and Particle Filters.Spectral Analysis
Periodogram.
Parametric Spectral Analysis.
AR Spectral Analysis.
MA Spectral Analysis.
ARMA Spectral Analysis.
Appendix: Which Sample Estimate of the Autocorrelation to Use?
Appendix: Eigenvectors and Eigenvalues of Correlation Matrix.
Appendix: Property of Monic Polynomial.
Appendix: Variance of Pole in AR(1).Adaptive Filtering
Adaptive Interference Cancellation.
Adaptive Equalization in Communication Systems.
Steepest Descent MSE Minimization.
From Iterative to Adaptive Filters.
LMS Algorithm and Stochastic Gradient.
Convergence Analysis of LMS Algorithm.
Learning Curve of LMS.
NLMS Updating and Non-Stationarity.
Numerical Example: Adaptive Identification.
RLS Algorithm.
Exponentially-Weighted RLS.
LMS vs. RLS.
Appendix: Convergence in Mean Square.Line Spectrum Analysis
Model Definition.
Maximum Likelihood and Cramér–Rao Bounds.
High-Resolution Methods.Equalization in Communication Engineering
Linear Equalization.
Non-Linear Equalization.
MIMO Linear Equalization.
MIMO–DFE Equalization.2D Signals and Physical Filters
2D Sinusoids.
2D Filtering.
Diffusion Filtering.
Laplace Equation and Exponential Filtering.
Wavefield Propagation.
Appendix: Properties of 2D Signals.
Appendix: Properties of 2D Fourier Transform.
Appendix: Finite Difference Method for PDE-Diffusion.Array Processing
Narrowband Model.
Beamforming and Signal Estimation.
DoA Estimation.Multichannel Time of Delay Estimation
Model Definition for ToD.
High Resolution Method for ToD (L=1).
Difference of ToD (DToD) Estimation.
Numerical Performance Analysis of DToD.
Wavefront Estimation: Non-Parametric Method (L=1).
Parametric ToD Estimation and Wideband Beamforming.
Appendix: Properties of the Sample Correlations.
Appendix: How to Delay a Discrete-Time Signal?
Appendix: Wavefront Estimation for 2D Arrays.Tomography
X-ray Tomography.
Algebraic Reconstruction Tomography (ART).
Reconstruction From Projections: Fourier Method.
Traveltime Tomography.
Internet (Network) Tomography.Cooperative Estimation
Consensus and Cooperation.
Distributed Estimation for Arbitrary Linear Models (p>1).
Distributed Synchronization.
Appendix: Basics of Undirected Graphs.Classifiation and Clustering
Historical Notes.
Classification.
Classification of Signals in Additive Gaussian Noise.
Bayesian Classification.
Pattern Recognition and Machine Learning.
Clustering.References
Index