Modern Signal Processing

Acknowledgements
1 Random Signals
    1.1 Signal Classifications
    1.2 Correlation Function, Covariance Function, and Power Spectral Density
        1.2.1 Autocorrelation Function, Autocovariance Function, and Power Spectral Density
        1.2.2 Cross Correlation Function, Cross Covariance Function, and Cross Power Spectral Density
    1.3 Comparison and Discrimination between Two Random Signals
        1.3.1 Independence, Uncorrelatedness, and Orthogonality
        1.3.2 Gram-Schmidt Orthogonalization Process of Polynomial Sequence
    1.4 Linear System with Random Input
        1.4.1 The Power Spectral Density of System Output
        1.4.2 Narrow Band Bandpass Filter
    Summary
    Exercises
2 Parameter Estimation Theory
    2.1 Performance of Estimators
        2.1.1 Unbiased and Asymptotic Unbiased Estimation
        2.1.2 Effectiveness of Estimators
    2.2 Fisher Information and Cramér-Rao Inequality
        2.2.1 Fisher Information
        2.2.2 Cramér-Rao Lower Bound
    2.3 Bayes Estimation
        2.3.1 Definition of Risk Function
        2.3.2 Bayes Estimation
    2.4 Maximum Likelihood Estimation
    2.5 Linear Mean Squares Estimation
    2.6 Least Squares Estimation
        2.6.1 Least Squares Estimation and Its Performance
        2.6.2 Weighted Least Squares Estimation
    Summary
    Exercises
3 Signal Detection
    3.1 Statistical Hypothesis Testing
        3.1.1 Basic Concepts of Signal Detection
        3.1.2 Signal Detection Measures
        3.1.3 Decision Space
    3.2 Probability Density Function and Error Function
        3.2.1 Probability Density Function
        3.2.2 Error Function and Complementary Error Function
    3.3 Probabilities of Detection and Error
        3.3.1 Definitions of Detection and Error Probabilities
        3.3.2 Power Function
    3.4 Neyman-Pearson Criterion
        3.4.1 Probabilities of False Alarm and Miss alarm in Radar Signal Detection
        3.4.2 Neyman-Pearson Lemma and Neyman-Pearson Criterion
    3.5 Uniformly Most Power Criterion
        3.5.1 Communication Signal Detection Problem
        3.5.2 Uniformly Most Power Test
        3.5.3 Physical Meaning of UMP Criterion
    3.6 Bayes Criterion
        3.6.1 Bayes Decision Criterion
        3.6.2 Detection of Binary Signal Waveform
        3.6.3 Detection Probability Analysis
    3.7 Bayes Derived Criteria
        3.7.1 Minimum Error Probability Criterion
        3.7.2 Maximum A Posteriori Probability Criterion
        3.7.3 Minimax Criterion
    3.8 Multivariate Hypotheses Testing
        3.8.1 Multivariate Hypotheses Testing Problem
        3.8.2 Bayes Criteria for Multiple Hypotheses Testing
    3.9 Multiple Hypothesis Testing
        3.9.1 Error Rate of Multiple Hypothesis Testing
        3.9.2 Error Control Method of Multiple Hypothesis Testing
        3.9.3 Multiple Linear Regression
        3.9.4 Multivariate Statistical Analysis
    Summary
    Exercises
4 Modern Spectral Estimation
    4.1 Nonparametric Spectral Estimation
        4.1.1 Discrete Stochastic Process
        4.1.2 Non-parametric Power Spectrum Estimation
    4.2 Stationary ARMA Process
    4.3 Power Spectral Density of Stationary Process
        4.3.1 Power Spectral Density of ARMA Process
        4.3.2 Power Spectrum Equivalence
    4.4 ARMA Spectrum Estimation
        4.4.1 Two Linear Methods for ARMA Power Spectrum Estimation
        4.4.2 Modified Yule-Walker Equation
        4.4.3 Singular Value Decomposition Method for AR Order Determination
        4.4.4 Total Least Squares Method for AR Parameter Estimation
    4.5 ARMA Model Identification
        4.5.1 MA Order Determination
        4.5.2 MA Parameter Estimation
    4.6 Maximum Entropy Spectrum Estimation
        4.6.1 Burg Maximum Entropy Spectrum Estimation
        4.6.2 Levinson Recursion
        4.6.3 Burg Algorithm
        4.6.4 Burg Maximum Entropy Spectrum Analysis and ARMA Spectrum Estimation
    4.7 Pisarenko Harmonic Decomposition Method
        4.7.1 Pisarenko Harmonic Decomposition
        4.7.2 ARMA Modeling Method for Harmonic Recovery
    4.8 Extended Prony Method
    Summary
    Exercises
5 Adaptive Filter
    5.1 Matched Filter
        5.1.1 Matched Filter
        5.1.2 Properties of Matched Filter
        5.1.3 Implementation of Matched Filter
    5.2 Continuous Time Wiener Filter
    5.3 Optimal Filtering Theory and Wiener Filter
        5.3.1 Linear Optimal Filter
        5.3.2 Orthogonality Principle
        5.3.3 Wiener Filter
    5.4 Kalman Filter
        5.4.1 Kalman Filtering Problem
        5.4.2 Innovation Process
        5.4.3 Kalman Filtering Algorithm
    5.5 LMS Adaptive Algorithms
        5.5.1 Descent Algorithm
        5.5.2 LMS Algorithm and Its Basic Variants
        5.5.3 Decorrelation LMS Algorithm
        5.5.4 Selection of the Learning Rate Parameter
        5.5.5 Statistical Performance Analysis of LMS Algorithm
        5.5.6 Tracking Performance of LMS Algorithm
    5.6 RLS Adaptive Algorithm
        5.6.1 RLS Algorithm
        5.6.2 Comparison between RLS Algorithm and Kalman Filtering Algorithm
        5.6.3 Statistical Performance Analysis of RLS Algorithm
        5.6.4 Fast RLS Algorithm
    5.7 Adaptive Line Enhancer and Notch Filter
        5.7.1 Transfer Functions of Line Enhancer and Notch Filter
        5.7.2 Adaptive Notch Filter based on Lattice IIR Filter
    5.8 Generalized Sidelobe Canceller
    5.9 Blind Adaptive Multiuser Detection
        5.9.1 Canonical Representation of Blind Multiuser Detection
        5.9.2 LMS and RLS Algorithms for Blind Multiuser Detection
        5.9.3 Kalman Adaptive Algorithm for Blind Multiuser Detection
    Summary
    Exercises
6 Higher-Order Statistical Analysis
    6.1 Moments and Cumulants
        6.1.1 Definition of Higher-order Moments and Cumulants
        6.1.2 Higher-order Moments and Cumulants of Gaussian Signal
        6.1.3 Transformation Relationships between Moments and Cumulants
    6.2 Properties of Moments and Cumulants
    6.3 Higher-order Spectra
        6.3.1 Higher-order Moment Spectra and Higher-order Cumulant Spectra
        6.3.2 Bispectrum Estimation
    6.4 Non-Gaussian Signal and Linear System
        6.4.1 Sub-Gaussian and Super-Gaussian Signal
        6.4.2 Non-Gaussian Signal Passing Through Linear System
    6.5 FIR System Identification
        6.5.1 RC Algorithm
        6.5.2 Cumulant Algorithm
        6.5.3 MA Order Determination
    6.6 Identification of Causal ARMA Models
        6.6.1 Identification of AR Parameters
        6.6.2 MA order Determination
        6.6.3 Estimation of MA Parameters
    6.7 Harmonic Retrieval in Colored Noise
        6.7.1 Cumulant Definition for Complex Signal
        6.7.2 Cumulants of Harmonic Process
        6.7.3 Harmonic Retrieval in Colored Gaussian Noise
        6.7.4 Harmonic Retrieval in Colored Non-Gaussian Noise
    6.8 The Adaptive Filtering of Non-Gaussian Signal
    6.9 Time Delay Estimation
        6.9.1 The Generalized Correlation Mehtod
        6.9.2 Higher-Order Statistics Method
    6.10 Application of Bispectrum in Signal Classification
        6.10.1 The Integrated Bispectra
        6.10.2 Selected Bispectra
    Summary
    Exercises
7 Linear Time-Frequency Transform
    7.1 Local Transformation of Signals
    7.2 Analytic Signal and Instantaneous Physical Quantity
        7.2.1 Analytic Signal
        7.2.2 Baseband Signal
        7.2.3 Instantaneous Frequency and Group Delay
        7.2.4 Exclusion Principle
    7.3 Short-Time Fourier Transform
        7.3.1 The Continuous Short-Time Fourier Transform
        7.3.2 The Discrete Short-Time Fourier Transform
    7.4 Gabor Transform
        7.4.1 The Continuous Gabor Transform
        7.4.2 The Discrete Gabor Transform
    7.5 Fractional Fourier transform
        7.5.1 Definition and Properties of Fractional Fourier Transform
        7.5.2 Calculation of Fractional Fourier Transform
    7.6 Wavelet Transform
        7.6.1 Physical Considerations of Wavelets
        7.6.2 The Continuous Wavelet Transform
        7.6.3 Discretization of Continuous Wavelet Transform
    7.7 Wavelet Analysis and Frame Theory
        7.7.1 Wavelet Analysis
        7.7.2 Frame Theory
    7.8 Multiresolution Analysis
    7.9 Orthogonal Filter Banks
        7.9.1 Orthogonal wavelet
        7.9.2 Fast Orthogonal Wavelet Transform
    7.10 Biorthgonal Filter Bank
        7.10.1 Biorthogonal Multiresolution Analysis
        7.10.2 Design of Biorthogonal Filter Banks
        7.10.3 Biorthogonal Wavelet and Fast Biorthogonal Transform
    Summary
    Exercises
8 Quadratic Time-frequency Distribution
    8.1 The General Theory of Time-frequency Distribution
        8.1.1 Definition of the Time-frequency Distribution
        8.1.2 Basic Properties of Time-frequency Distribution
    8.2 The Wigner-Ville Distribution
        8.2.1 Mathematical Properties
        8.2.2 Relationship to Evolutive Spectrum
        8.2.3 Signal Reconstruction based on Wigner-Ville Distribution
    8.3 Ambiguity Function
    8.4 Cohen’s Class Time-frequency Distribution
        8.4.1 Definition of Cohen’s Class Time-frequency Distribution
        8.4.2 Requirements for Kernel Function
    8.5 Performance Evaluation and Improvement of Time-frequency Distribution
        8.5.1 Time-frequency Aggregation
        8.5.2 Cross-Term Suppression
        8.5.3 Other Typical Time-frequency Distributions
    Summary
    Exercises
9 Blind Signal Separation
    9.1 Basic Theory of Blind Signal Processing
        9.1.1 A Brief Introduction to Blind Signal Processing
        9.1.2 Model and Basic Problem of BSS
        9.1.3 Basic Assumption and Performance Requirement of BSS
    9.2 Adaptive Blind Signal Separation
        9.2.1 Neural Network Implementation of Adaptive Blind Signal Separation
        9.2.2 Quasiidentity Matrix and Contrast Function
    9.3 Indenpent Component Analysis
        9.3.1 Mutual Information and Negentropy
        9.3.2 Natural Gradient Algorithm
        9.3.3 Implementation of the Natural Gradient Algorithm
        9.3.4 Fixed-Point Algorithm
    9.4 Nonlinear Principal Component Analysis
        9.4.1 Pre-whitening
        9.4.2 Linear Principal Component Analysis
        9.4.3 Nonlinear Principal Component Analysis
    9.5 Joint Diagonalization of Matrices
        9.5.1 Blind Signal Separation and Joint Diagonalization of Matrices
        9.5.2 Orthogonal Approximate Joint Diagonalization
        9.5.3 Nonorthogonal Approximate Joint Diagonalization
    9.6 Blind Signal Extraction
        9.6.1 Orthognal Blind Signal Extraction
        9.6.2 Nonorthogonal Blind Signal Extraction
    9.7 Blind Signal Separation of Convolutively Mixed Sources
        9.7.1 Convolutively Mixed Sources
        9.7.2 Time Domain Blind Signal Separation of Convolutively Mixed Sources
        9.7.3 Frequency Domain Blind Signal Separation of Convolutively Mixed Sources
        9.7.4 Time-Frequency Domain Blind Signal Separation of Convolutively Mixed Sources
    Summary
    Exercises
10 Array Signal Processing
    10.1 Coordinate Representation of Array
        10.1.1 Array and Noise
        10.1.2 Coordinate System of Array
    10.2 Beamforming and Spatial Filtering
        10.2.1 Spatial FIR Filter
        10.2.2 Broadband Beamformer
        10.2.3 Analogy and Interchange between Spatial FIR Filter and Beamformer
    10.3 Linearly-Constrained Adaptive Beamformer
        10.3.1 Classical Beamforming
        10.3.2 Direct Implementation of Adaptive Beamforming
        10.3.3 Generlized Sidelobe Canceling Form of Adaptive Beamforming
    10.4 Multiple Signal Classification (MUSIC)
        10.4.1 Spatial Spectrum
        10.4.2 Signal Subspace and Noise Subspace
        10.4.3 MUSIC Algorithm
    10.5 Extensions of MUSIC Algorithm
        10.5.1 Decoherent MUSIC Algorithm
        10.5.2 Root-MUSIC Algorithm
        10.5.3 Minimum Norm Algorithm
        10.5.4 First Principal Vector MUSIC Algorithm
    10.6 Beamspace MUSIC Algorithm
        10.6.1 BS-MUSIC Algorithm
        10.6.2 Comparison of BS-MUSIC and ES-MUSIC
    10.7 Estimating Signal Parameters via Rotational Invariance Techniques
        10.7.1 Basic ESPRIT Algorithm
        10.7.2 Element Space ESPRIT
        10.7.3 TLS-ESPRIT
        10.7.4 Beamspace ESPRIT Algorithm
    10.8 Unitary ESPRIT and Its Extensions
        10.8.1 Unitary ESPRIT Algorithm
        10.8.2 Beamspace Unitary ESPRIT Algorithm
    Summary
    Exercises
Index
Bibliography