For upper-level undergraduate courses in deterministic and stochastic signals and system engineering
An Integrative Approach to Signals, Systems and Inference
Signals, Systems and Inference is a comprehensive text that builds on introductory courses in time- and frequency-domain analysis of signals and systems, and in probability. Directed primarily to upper-level undergraduates and beginning graduate students in engineering and applied science branches, this new textbook pioneers a novel course of study. Instead of the usual leap from broad introductory subjects to highly specialized advanced subjects, this engaging and inclusive text creates a study track for a transitional course. Properties and representations of deterministic signals and systems are reviewed and elaborated on, including group delay and the structure and behavior of state-space models.
The text also introduces and interprets correlation functions and power spectral densities for describing and processing random signals. Application contexts include pulse amplitude modulation, observer-based feedback control, optimum linear filters for minimum mean-square-error estimation, and matched filtering for signal detection. Model-based approaches to inference are emphasized, in particular for state estimation, signal estimation, and signal detection. The text explores ideas, methods and tools common to numerous fields involving signals, systems and inference: signal processing, control, communication, time-series analysis, financial engineering, biomedicine, and many others. Signals, Systems, and Inference is a long-awaited and flexible text that can be used for a rigorous course in a broad range of engineering and applied science curricula.
Preface The Cover Acknowledgments Prologue 1. Signals and Systems 1.1 Signals, Systems, Models, and Properties 1.1.1 System Properties 1.2 Linear, Time-Invariant Systems 1.2.1 Impulse-Response Representation of LTI Systems 1.2.2 Eigenfunction and Transform Representation of LTI Systems 1.2.3 Fourier Transforms 1.3 Deterministic Signals and Their Fourier Transforms 1.3.1 Signal Classes and Their Fourier Transforms 1.3.2 Parseval's Identity, Energy Spectral Density, and Deterministic Autocorrelation 1.4 Bilateral Laplace and Z-Transforms 1.4.1 The Bilateral z-Transform 1.4.2 The Bilateral Laplace Transform 1.5 Discrete-Time Processing of Continuous-Time Signals 1.5.1 Basic Structure for DT Processing of CT Signals 1.5.2 DT Filtering and Overall CT Response 1.5.3 Nonideal D/C Converters 1.6 Further Reading Problems Basic Problems Advanced Problems Extension Problems 2. Amplitude, Phase, and Group Delay 2.1 Fourier Transform Magnitude and Phase 2.2 Group Delay and the Effect of Nonlinear Phase 2.2.1 Narrowband Input Signals 2.2.2 Broadband Input Signals 2.3 All-Pass and Minimum-Phase Systems 2.3.1 All-Pass Systems 2.3.2 Minimum-Phase Systems 2.3.3 The Group Delay of Minimum-Phase Systems 2.4 Spectral Factorization 2.5 Further Reading Problems Basic Problems Advanced Problems Extension Problems 3. Pulse-Amplitude Modulation 3.1 Baseband Pulse-Amplitude Modulation 3.1.1 The Transmitted Signal 3.1.2 The Received Signal 3.1.3 Frequency-Domain Characterizations 3.1.4 Intersymbol Interference at the Receiver 3.2 Nyquist Pulses 3.3 Passband Pulse-Amplitude Modulation 3.3.1 Frequency-Shift Keying (FSK) 3.3.2 Phase-Shift Keying (PSK) 3.3.3 Quadrature-Amplitude Modulation (QAM) 3.4 Further Reading Problems Basic Problems Advanced Problems Extension Problems 4. State-Space Models 4.1 System Memory 4.2 Illustrative Examples 4.3 State-Space Models 4.3.1 DT State-Space Models 4.3.2 CT State-Space Models 4.3.3 Defining Properties of State-Space Models 4.4 State-Space Models from LTI Input-Output Models 4.5 Equilibria and Linearization of Nonlinear State-Space Models 4.5.1 Equilibrium 4.5.2 Linearization 4.6 Further Reading Problems Basic Problems Advanced Problems Extension Problems 5. LTI State-Space Models 5.1 Continuous-Time and Discrete-Time LTI Models 5.2 Zero-Input Response and Modal Representation 5.2.1 Undriven CT Systems 5.2.2 Undriven DT Systems 5.2.3 Asymptotic Stability of LTI Systems 5.3 General Response in Modal Coordinates 5.3.1 Driven CT Systems 5.3.2 Driven DT Systems 5.3.3 Similarity Transformations and Diagonalization 5.4 Transfer Functions, Hidden Modes, Reachability, and Observability 5.4.1 Input-State-Output Structure of CT Systems 5.4.2 Input-State-Output Structure of DT Systems 5.5 Further Reading Problems Basic Problems Advanced Problems Extension Problems 6. State Observers and State Feedback 6.1 Plant and Model 6.2 State Estimation and Observers 6.2.1 Real-Time Simulation 6.2.2 The State Observer 6.2.3 Observer Design 6.3 State Feedback Control 6.3.1 Open-Loop Control 6.3.2 Closed-Loop Control via LTI State Feedback 6.3.3 LTI State Feedback Design 6.4 Observer-Based Feedback Control 6.5 Further Reading Problems Basic Problems Advanced Problems Extension Problems 7. Probabilistic Models 7.1 The Basic Probability Model 7.2 Conditional Probability, Bayes' Rule, and Independence 7.3 Random Variables 7.4 Probability Distributions 7.5 Jointly Distributed Random Variables 7.6 Expectations, Moments, and Variance 7.7 Correlation and Covariance for Bivariate Random Variables 7.8 A Vector-Space Interpretation of Correlation Properties 7.9 Further Reading Problems Basic Problems Advanced Problems Extension Problems 8. Estimation 8.1 Estimation of a Continuous Random Variable 8.2 From Estimates to the Estimator 8.2.1 Orthogonality 8.3 Linear Minimum Mean Square Error Estimation 8.3.1 Linear Estimation of One Random Variable from a Single Measurement of Another 8.3.2 Multiple Measurements 8.4 Further Reading Problems Basic Problems Advanced Problems Extension Problems 9. Hypothesis Testing 9.1 Binary Pulse-Amplitude Modulation in Noise 9.2 Hypothesis Testing with Minimum Error Probability 9.2.1 Deciding with Minimum Conditional Probability of Error 9.2.2 MAP Decision Rule for Minimum Overall Probability of Error 9.2.3 Hypothesis Testing in Coded Digital Communication 9.3 Binary Hypothesis Testing 9.3.1 False Alarm, Miss, and Detection 9.3.2 The Likelihood Ratio Test 9.3.3 Neyman-Pearson Decision Rule and Receiver Operating Characteristic 9.4 Minimum Risk Decisions 9.5 Further Reading Problems Basic Problems Advanced Problems Extension Problems 10. Random Processes 10.1 Definition and Examples of a Random Process 10.2 First- and Second-Moment Characterization of Random Processes 10.3 Stationarity 10.3.1 Strict-Sense Stationarity 10.3.2 Wide-Sense Stationarity 10.3.3 Some Properties of WSS Correlation and Covariance Functions 10.4 Ergodicity 10.5 Linear Estimation of Random Processes 10.5.1 Linear Prediction 10.5.2 Linear FIR Filtering 10.6 LTI Filtering of WSS Processes 10.7 Further Reading Problems Basic Problems Advanced Problems Extension Problems 11. Power Spectral Density 11.1 Spectral Distribution of Expected Instantaneous Power 11.1.1 Power Spectral Density 11.1.2 Fluctuation Spectral Density 11.1.3 Cross-Spectral Density 11.2 Expected Time-Averaged Power Spectrum and the Einstein-Wiener-Khinchin Theorem 11.3 Applications 11.3.1 Revealing Cyclic Components 11.3.2 Modeling Filters 11.3.3 Whitening Filters 11.3.4 Sampling Bandlimited Random Processes 11.4 Further Reading Problems Basic Problems Advanced Problems Extension Problems 12. Signal Estimation 12.1 LMMSE Estimation for Random Variables 12.2 FIR Wiener Filters 12.3 The Unconstrained DT Wiener Filter 12.4 Causal DT Wiener Filtering 12.5 Optimal Observers and Kalman Filtering 12.5.1 Causal Wiener Filtering of a Signal Corrupted by Additive Noise 12.5.2 Observer Implementation of the Wiener Filter 12.5.3 Optimal State Estimates and Kalman Filtering 12.6 Estimation of CT Signals 12.7 Further Reading Problems Basic Problems Advanced Problems Extension Problems 13. Signal Detection 13.1 Hypothesis Testing with Multiple Measurements 13.2 Detecting a Known Signal in I.I.D. Gaussian Noise 13.2.1 The Optimal Solution 13.2.2 Characterizing Performance 13.2.3 Matched Filtering 13.3 Extensions of Matched-Filter Detection 13.3.1 Infinite-Duration, Finite-Energy Signals 13.3.2 Maximizing SNR for Signal Detection in White Noise 13.3.3 Detection in Colored Noise 13.3.4 Continuous-Time Matched Filters 13.3.5 Matched Filtering and Nyquist Pulse Design 13.3.6 Unknown Arrival Time and Pulse Compression 13.4 Signal Discrimination in I.I.D. Gaussian Noise 13.5 Further Reading Problems Basic Problems Advanced Problems Extension Problems Bibliography Index