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Separate signals from noise with this valuable introduction to signal processing by applied decomposition
The decomposition of complex signals into the sub-signals, or individual components, is a crucial tool in signal processing. It allows each component of a signal to be analyzed individually, enables the signal to be isolated from noise, and processed in full. Decomposition processes have not always been widely adopted due to the difficult underlying mathematics and complex applications. This text simplifies these obstacles.
Signal Processing: An Applied Decomposition Approach demystifies these tools from a model-based perspective. This offers a mathematically informed, “step-by-step” analysis of the process by breaking down a composite signal/system into its constituent parts, while introducing both fundamental concepts and advanced applications. This comprehensive approach addresses each of the major decomposition techniques, making it an indispensable addition to any library specializing in signal processing.
Signal Processing readers will find:
Signal decomposition techniques developed from the data-based, spectral-based and model-based perspectives incorporate: statistical approaches (PCA, ICA, Singular Spectrum); spectral approaches (MTM, PHD, MUSIC); and model-based approaches (EXP, LATTICE, SSP)In depth discussion of topics includes signal/system estimation and decomposition, time domain and frequency domain techniques, systems theory, modal decompositions, applications and many more Numerous figures, examples, and tables illustrating key concepts and algorithms are developed throughout the text Includes problem sets, case studies, real-world applications as well as MatLAB notes highlighting applicable commands
Signal Processing is ideal for engineering and scientific professionals, as well as graduate students seeking a focused text on signal/system decomposition with performance metrics and real-world applications.
About the Author
Preface
Acknowledgments
Glossary
About the Companion Website
Introduction
Background
Spectral Decomposition
Data Decomposition
Model-based Decomposition
Notation and Terminology
Summary
MatLAB Notes
References
Problems
Random Signals and Systems
Introduction
Discrete Random Signals
Spectral Representation of Random Signals
Discrete Systems with Random Inputs
Classical Spectral Estimation
Correlation Method (Blackman–Tukey)
Average Periodogram Method (Welch)
Minimum Variance Distortionless Response (MVDR)
Coherence Function
Case Study: Sinusoids in Noise
Summary
MatLAB Notes
References
Problems
Signal Models
Data-Based Models
Data-Based Response Matrices
Data-Based Toeplitz Matrices
Data-Based Hankel Matrices
Parametric-Based Models
ARMAX (AR, ARX, MA, ARMA) Models
Lattice Models
Transfer Function/Frequency Response Function Models
Harmonic Models
State-space Models
Continuous-time State-space Models
Sampled-data State-space Models
Discrete-time State-space Models
Gauss–Markov State-space Models
Innovations Model
State-space Equivalence Models
Summary
MatLAB Notes
References
Problems
Signal Estimation
Classical Estimation
Estimator Properties
Estimator Performance
Minimum Variance (MV) Estimation
Maximum A-Posteriori (MAP) Estimation
Maximum Likelihood (ML) Estimation
Least-squares (LS) Estimation
Batch Least Squares
Recursive Least-squares
Optimal Signal Estimation
Projection Theory
Orthogonal Projections: A Geometric Decomposition Perspective
Orthogonal Projections: Singular Value Decomposition
Summary
MatLAB Notes
References
Problems
Signal Decomposition
Introduction
Data-Based Decompositions
Data Decomposition: Principal Component Analysis (PCA)
Data Decomposition: Independent Component Analysis (ICA)
Higher Order Statistics
Information Theory: Negentropy
Information Theory: Mutual Information
Estimation Theory: Maximum Likelihood
Data Decomposition: Singular Spectral Analysis (SSA)
Spectral-Based Decompositions
Spectral Decomposition: Multitaper Method (MTM)
Spectral Decomposition: Subspace Method
Spectral Decomposition: Pisarenko Harmonic Decomposition (PHD) Method
Spectral Decomposition: Multiple Signal Classification (MUSIC) Method
Model-Based Decomposition
Model-Based Decomposition: Damped Exponential Method
Model-Based Decomposition: Lattice Method
Model-Based Decomposition: State-Space Method
Case Study: Harmonics in Noise
Summary
MatLAB Notes
References
Problems
Model-based Decomposition: Time Domain
Background: State-space Systems
Discrete Systems Theory
Stable Linear Systems
Equivalent Linear Systems
Modal Systems
Realization Problem
Realization Theory
Balanced Realizations
Systems Theory Summary
Realization Decomposition
Ho–Kalman Realization
SVD Realization
Subspace Decomposition: Orthogonal Projections
Subspace Realization: Orthogonal Projections
Multivariable Output Error State-space (MOESP) Algorithm
Subspace Decomposition: Oblique Projections
Subspace Realization: Oblique Projections
Numerical Algorithms for Subspace State-space System Identification (NSID)
System Order Estimation and Validation
Order Estimation: SVD Approach
Model Validation
Case Study: Multichannel Mechanical Systems
Mechanical Systems
Case Study: -mass Mechanical System
Summary
MatLAB Notes
References
Problems
Model-Based Decomposition: Frequency Domain
Introduction
Background
Frequency Response Functions (FRF)
FRF Estimation: Impulse Response Method
FRF Spectral Estimation: Polynomial Models
FRF-Spectral Estimation: Power Spectra
FRF-Spectral Estimation: Frequency Domain Decomposition (FDD) Method
Power Spectral Density Decomposition
Complex Mode Indicator Function (CMIF)
Stabilization Diagram (SDIAG)
Least-squares Complex Frequency (LSCF) Method
PolyReference Least-Squares Complex Frequency (pLSCF) Method
Maximum Likelihood PolyReference Frequency Domain Estimation (ML-pLSCF)
Case Study: -DOF Structure
Summary
MatLAB Notes
References
Problems
Performance Analysis
Statistical Performance Methods
Zero-Mean Test
Whiteness Test
Weighted Sum-Squared Residual Test
Standard Error Test
Correlation Coefficient Function Test
Coherence Function Test
Ensemble Tests
Statistical Order Estimation
Signal (Model) Validation
MAD Signal Validation
Physical Performance Metrics
Spectral Peaks: Picking/Histogram
Modal Assurance Criterion (MAC)
Hankel/SVD Criteria
Modal Observability Correlation (MOC) Criterion
Modal Singular Value (MSV) Criterion
Stabilization Diagram (SDIAG)
Modal Frequency Tracker
Case Study: Resonant Modal MCK System
Summary
MatLAB Notes
References
Applications
Modal Decomposition: Sounding Rocket Flight
Experimental Test Unit Design and Analysis
Sounding Rocket Flight Testing
Summary
Vibrational Response of a Cylindrical Structure: Identification and Modal Tracking
Summary
Resonant Ultrasound Spectroscopy
RUS Methodology
Modal Analysis: FRF and Frequency Histogram
Model-Based Decomposition Approach
Application: Parallel Piped Structure
Synthesized Data: RPP Structure
Experimental Data: RPP Structure
Model-Based Decomposition Processor
Elastic Coefficient Estimation
Summary
Model-Based Subsystem Decomposition of an -Story (-Mass) Structure
Subspace Structural Identification
Shaping Filters
Subsystem Modal Extraction
Summary
Data-Based Decomposition: Time-Reversal Processing
Iterative Time-Reversal Decomposition
Eigen-decomposition Time-reversal Extraction
Summary
References
Probability and Statistics Overview
Probability Theory
Gaussian Random Vectors
Uncorrelated Transformation: Gaussian Random Vectors
Toeplitz Correlation Matrices
Important Processes
References
Projection Theory
Projections: Deterministic Spaces
Projections: Random Spaces
Projection: Operators
Orthogonal (Perpendicular) Projections
Oblique (Parallel) Projections
References
Matrix Decompositions
Singular Value Decomposition
QR Decomposition
LQ Decomposition
References
Index