Signals, Systems and Inference, 1st edition
Published by Unknown (April 1, 2015) © 2016
- Alan V Oppenheim
- George C. Verghese Massachusetts Institute of Technology
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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.
Signals, Systems and Inference facilitates learning with the following features.
A text structure that is highly organized and easy to navigate
- The text is divided into four major parts:
- Chapters 1-3 present a reviewof the assumed prerequisite notions in signals and systems, and apply these to digital communication by pulse amplitude modulation.
- Chapters 4-6 treat space-state models,
- concentrating on the single-input single-output LTI case;
- introducing the idea of model-based inference;
- examining associated feedback control strategies.
- Chapters 7-9 provide a review of assumed prerequisites in probability, including estimation and hypothesis testing for static random variables.
- Chapters 10-13 explore wide-sense stationary random signals and their processing by LTI systems for various applications.
- The properties and interpretations of correlation functions and power spectral densities are developed in Chapters 10-11,and used in the remaining chapters to study canonical inference problems in signal estimation and signal detection.
- Chapter 12 focuses on Wiener filtering, or linear minimum mean square error signal estimation.
- Chapter 13Â emphasizes signal detection problems for which the optimum solutions involve matched filtering.
Thorough and interesting chapters full of information
- An exploration of fundamental material in an interesting and engaging manner.
- Further Reading sections at the end of each chapter help students gain further knowledge of the subject matter.
- Basic, Advanced, and Extensionproblems that review chapter material and ask the students to test and apply their knowledge of the subject.
A flexible approach to a broad course of study
- Since there is more material in this text than can comfortably be taught in a one-semester course, the text allows for different routes of instruction that emphasize various paths of study.
- Chapters 4-6Â can be omitted or only briefly addressed in courses oriented towards communication and signal processing.
- Chapters 3, 9 and 13Â can be considered optional for courses with more of a control orientation.
A course that includes core material from every chapter can be taught with two weekly lectures and associated small group discussions over an approximately 13-week semester.
Preface
The Cover
Acknowledgments
Prologue
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Bibliography
Index
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