- Cover
- Title Page
- 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?
- 1 Manipulations on Matrixes
- 2 Linear Algebraic Systems
- 2.1 Problem Definition and Vector Spaces
- 2.2 Rotations
- 2.3 Projection Matrixes and Data‐Filtering
- 2.4 Singular Value Decomposition (SVD) and Subspaces
- 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
- 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
- 3.8 Sum of Square of Gaussians: Chi‐Square
- 3.9 Order Statistics for N rvs
- 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)
- 4.5 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
- 5 Models and Applications
- 6 Estimation Theory
- 7 Parameter Estimation
- 8 Cramér–Rao Bound
- 9 MLE and CRB for Some Selected Cases
- 10 Numerical Analysis and Montecarlo Simulations
- 11 Bayesian Estimation
- 12 Optimal Filtering
- 13 Bayesian Tracking and Kalman Filter
- 14 Spectral Analysis
- 14.1 Periodogram
- 14.2 Parametric Spectral Analysis
- 14.3 AR Spectral Analysis
- 14.4 MA Spectral Analysis
- 14.5 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)
- 15 Adaptive Filtering
- 15.1 Adaptive Interference Cancellation
- 15.2 Adaptive Equalization in Communication Systems
- 15.3 Steepest Descent MSE Minimization
- 15.4 From Iterative to Adaptive Filters
- 15.5 LMS Algorithm and Stochastic Gradient
- 15.6 Convergence Analysis of LMS Algorithm
- 15.7 Learning Curve of LMS
- 15.8 NLMS Updating and Non‐Stationarity
- 15.9 Numerical Example: Adaptive Identification
- 15.10 RLS Algorithm
- 15.11 Exponentially‐Weighted RLS
- 15.12 LMS vs. RLS
- Appendix A: Convergence in Mean Square
- 16 Line Spectrum Analysis
- 17 Equalization in Communication Engineering
- 18 2D Signals and Physical Filters
- 19 Array Processing
- 20 Multichannel Time of Delay Estimation
- 20.1 Model Definition for ToD
- 20.2 High Resolution Method for ToD (L = 1)
- 20.3 Difference of ToD (DToD) Estimation
- 20.4 Numerical Performance Analysis of DToD
- 20.5 Wavefront Estimation: Non‐Parametric Method (L = 1)
- 20.6 Parametric ToD Estimation and Wideband Beamforming
- Appendix A: Properties of the Sample Correlations
- Appendix B: How to Delay a Discrete‐Time Signal?
- Appendix C: Wavefront Estimation for 2D Arrays
- 21 Tomography
- 22 Cooperative Estimation
- 23 Classification and Clustering
- References
- Index
- End User License Agreement
Statistical Signal Processing in Engineering
Umberto Spagnolini
Politecnico di Milano
Italy
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