CHAPTER 1 Introduction

1.1 What Is a Signal?

1.2 What Is a System?

1.3 Overview of Specific Systems

1.4 Classification of Signals

1.5 Basic Operations on Signals

1.6 Elementary Signals

1.7 Systems Viewed as Interconnections of Operations

1.8 Properties of Systems

1.9 Noise

1.10 Theme Examples

1.11 Exploring Concepts with MATLAB

1.12 Summary

Further Reading

Additional Problems

CHAPTER 2 Time-Domain Representations of Linear Time-Invariant Systems

2.1 Introduction

2.2 The Convolution Sum

2.3 Convolution Sum Evaluation Procedure

2.4 The Convolution Integral

2.5 Convolution Integral Evaluation Procedure

2.6 Interconnections of LTI Systems

2.7 Relations between LTI System Properties and the Impulse Response

2.8 Step Response

2.9 Differential and Difference Equation Representations of LTI Systems

2.10 Solving Differential and Difference Equations

2.11 Characteristics of Systems Described by Differential and Difference Equations

2.12 Block Diagram Representations

2.13 State-Variable Descriptions of LTI Systems

2.14 Exploring Concepts with MATLAB

2.15 Summary

Further Reading

Additional Problems

CHAPTER 3 Fourier Representations of Signals and Linear Time-Invariant Systems

3.1 Introduction

3.2 Complex Sinugoids and Frequency Response of LTI Systems

3.3 Fourier Representations for Four Classes of Signals

3.4 Discrete-Time Periodic Signals: The Discrete-Time Fourier Series

3.5 Continuous-Time Periodic Signals: The Fourier Series

3.6 Discrete-Time Nonperiodic Signals: The Discrete-Time Fourier Transform

3.7 Continuous-Time Nonperiodic Signals: The Fourier Transform

3.8 Properties of Fourier Representations

3.9 Linearity and Symmetry Properties

3.10 Convolution Property

3.11 Differentiation and Integration Properties

3.12 Time- and Frequency-Shift Properties

3.13 Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions

3.14 Multiplication Property

3.15 Scaling Properties

3.16 Parseval Relationships

3.17 Time-Bandwidth Product

3.18 Duality

3.19 Exploring Concepts with MATLAB

3.20 Summary

Further Reading

Additional Problems

CHAPTER 4 Applications of Fourier Representations to Mixed Signal Classes

4.1 Introduction

4.2 Fourier Transform Representations of Periodic Signals

4.3 Convolution and Multiplication with Mixtures of Periodic and Nonperiodic Signals

4.4 Fourier Transform Representation of Discrete-Time Signals

4.5 Sampling

4.6 Reconstruction of Continuous-Time Signals from Samples

4.7 Discrete-Time Processing of Continuous-Time Signals

4.8 Fourier Series Representations of Finite-Duration Nonperiodic Signals

4.9 The Discrete-Time Fourier Series Approximation to the Fourier Transform

4.10 Efficient Algorithms for Evaluating the DTFS

4.11 Exploring Concepts with MATLAB

4.12 Summary

Further Reading

Additional Problems

CHAPTER 5 Application to Communication Systems

5.1 Introduction

5.2 Types of Modulation

5.3 Benefits of Modulation

5.4 Full Amplitude Modulation

5.5 Double Sideband-Suppressed Carrier Modulation

5.6 Quadrature-Carrier Multiplexing

5.7 Other Variants of Amplitude Modulation

5.8 Pulse-Amplitude Modulation

5.9 Multiplexing

5.10 Phase and Group Delays

5.11 Exploring Concepts with MATLAB

5.12 Summary

Further Reading

Additional Problems

CHAPTER 6 Representing Signals by Using Continuous-TimeComplex Exponentials: the Laplace Transform

6.1 Introduction

6.2 The Laplace Transform

6.3 The Unilateral Laplace Transform

6.4 Properties of the Unilateral Laplace Transform

6.5 Inversion of the Unilateral Laplace Transform

6.6 Solving Differential Equations with Initial Conditions

6.7 Laplace Transform Methods in Circuit Analysis

6.8 Properties of the Bilateral Laplace Transform

6.9 Properties of the Region of Convergence

6.10 Inversion of the Bilateral Laplace Transform

6.11 The Transfer Function

6.12 Causality and Stability

6.13 Determining the Frequency Response from Poles and Zeros

6.14 Exploring Concepts with MATLAB

6.15 Summary

Further Reading

Additional Problems

CHAPTER 7 Representing Signals by Using Discrete-Time Complex Exponentials: the z-Transform

7.1 Introduction

7.2 The z-Transform

7.3 Properties of the Region of Convergence

7.4 Properties of the z-Transform

7.5 Inversion of the z-Transform

7.6 The Transfer Function

7.7 Causality and Stability

7.8 Determining the Frequency Response from Poles and Zeros

7.9 Computational Structures for Implementing Discrete-Time LTI Systems

7.10 The Unilateral z-Transform

7.11 Exploring Concepts with MATLAB

7.12 Summary

Further Reading

Additional Problems

CHAPTER 8 Application to Filters and Equalizers

8.1 Introduction

8.2 Conditions for Distortionless Transmission

8.3 Ideal Low-Pass Filters

8.4 Design of Filters

8.5 Approximating Functions

8.6 Frequency Transformations

8.7 Passive Filters

8.8 Digital Filters

8.9 FIR Digital Filters

8.10 IIR Digital Filters

8.11 Linear Distortion

8.12 Equalization

8.13 Exploring Concepts with MATLAB

8.14 Summary

Further Reading

Additional Problems

CHAPTER 9 Application to Linear Feedback Systems

9.1 Introduction

9.2 What Is Feedback?

9.3 Basic Feedback Concepts

9.4 Sensitivity Analysis

9.5 Effect of Feedback on Disturbance or Noise

9.6 Distortion Analysis

9.7 Summarizing Remarks on Feedback

9.8 Operational Amplifiers

9.9 Control Systems

9.10 Transient Response of Low-Order Systems

9.11 The Stability Problem

9.12 Routh-Hurwitz Criterion

9.13 Root Locus Method

9.14 Nyquist Stability Criterion

9.15 Bode Diagram

9.16 Sampled-Data Systems

9.17 Exploring Concepts with MATLAB

9.18 Summary

Further Reading

Additional Problems

CHAPTER 10 Epilogue

10.1 Introduction

10.2 Speech Signals: An Example of Nonstationarity

10.3 Time-Frequency Analysis

10.4 Nonlinear Systems

10.5 Adaptive Filters

10.6 Concluding Remarks

Further Reading

APPENDIX A Selected Mathematical Identities

A.1 Trigonometry

A.2 Complex Numbers

A.3 Geometric Series

A.4 Definite Integrals

A.5 Matrices

APPENDIX B Partial-Fraction Expansions

B.1 Partial-Fraction Expansions of Continuous-TimeRepresentations

B.2 Partial-Fraction Expansions of Discrete-TimeRepresentation

APPENDIX C Tables of Fonrier Representations and Properties

C.1 Basic Discrete-Time Fourier Series Pairs

C.2 Basic Fourier Series Pairs

C.3 Basic Discrete-Time Fourier Transform Pairs

C.4 Basic Fourier Transform Pairs

C.5 Fourier Transform Pairs for Periodic Signals

C.6 Discrete-Time Fourier Transform Pairs for Periodic Signals

C.7 Properties of Fourier Representations

C.8 Relating the Four Fourier Representations

C.9 Sampling and Aliasing Relationships

APPENDIX D Tables of Laplace Transforms and Properties

D.1 Basic Laplace Transforms

D.2 Laplace Transform Properties

APPENDIX E Tables of z-Tansforms and Properties

E.1 Basic z-Transforms

E.2 z-Transform Properties

APPENDIX F Introduction to MATLAB

F.1 Basic Arithmetic Rules

F.2 Variables and Variable Names

F.3 Vectors and Matrices

F.4 Plotting in MATLAB

F.5 M-files

F.6 Additional Help

INDEX