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

Signals, Systems and Inference, 1st edition

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