Dedication

Preface

Acknowledgments

1: Introduction

0: From the Ground Up!

0.1 Introduction

0.2 Examples of Signal Processing Applications

0.3 Continuous or Discrete?

0.4 Complex or Real?

0.5 Soft Introduction to MATLAB

0.6 Problems

2: Theory and Application of Continuous-Time Signals and Systems

1: Continuous-time Signals

1.1 Introduction

1.2 Classification of Time-Dependent Signals

1.3 Continuous-Time Signals

1.4 Representation of Continuous-Time Signals Using Basic Signals

1.5 Special Signals—the Sampling and the Sinc Signals

1.6 Basic Signal Operations—Time Scaling, Frequency Shifting, and Windowing

1.7 What Have We Accomplished? Where Do We Go from Here?

1.8 Problems

2: Continuous-time Systems

2.1 Introduction

2.2 System Concept and Classification

2.3 Linear Time-invariant (LTI) Continuous-time Systems

2.4 Causality

2.5 Bounded-input Bounded-output (BIBO) Stability

2.6 What Have We Accomplished? Where Do We Go From Here?

2.7 Problems

3: The Laplace Transform

3.1 Introduction

3.2 The Two-sided Laplace Transform

3.3 The One-sided Laplace Transform

3.4 Properties of the One-sided Laplace Transform

3.5 Inverse Laplace Transform

3.6 Analysis of LTI Systems

3.7 What Have We Accomplished? Where Do We Go from Here?

3.8 Problems

4: Frequency Analysis: The Fourier Series

4.1 Introduction

4.2 Eigenfunctions Revisited

4.3 Complex Exponential Fourier Series

4.4 Response of LTI Systems to Periodic Signals

4.5 Operations using Fourier Series

4.6 What have We Accomplished? Where Do We Go from here?

4.7 Problems

5: Frequency Analysis: The Fourier Transform

5.1 Introduction

5.2 From the Fourier Series to the Fourier Transform

5.3 Existence of the Fourier Transform

5.4 Fourier Transforms from the Laplace Transform

5.5 Linearity, Inverse Proportionality, and Duality

5.6 Spectral Representation

5.7 Convolution and Filtering

5.8 Additional Properties

5.9 What Have we Accomplished? What is Next?

5.10 Problems

6: Application of Laplace Analysis to Control

6.1 Introduction

6.2 System Connections and Block Diagrams

6.3 Application to Classical Control

6.4 State-variable Representation of LTI Systems

6.5 What Have we Accomplished? What is Next?

6.6 Problems

7: Fourier Analysis in Communications and Filtering

7.1 Introduction

7.2 Application to Communications

7.3 Analog Filtering

7.4 What have We Accomplished? What is Next?

7.5 Problems

3: Theory and Application of Discrete-Time Signals and Systems

8: Sampling Theory

8.1 Introduction

8.2 Uniform Sampling

8.3 Practical Aspects of Sampling

8.4 Application to Digital Communications

8.5 What Have We Accomplished? Where Do We Go from Here?

8.6 Problems

9: Discrete-time Signals and Systems

9.1 Introduction

9.2 Discrete-Time Signals

9.3 Discrete-Time Systems

9.4 What Have We Accomplished? Where Do We Go From Here?

9.5 Problems

10: The Z-transform

10.1 Introduction

10.2 Laplace Transform of Sampled Signals

10.3 Two-sided Z-transform

10.4 One-sided Z-transform

10.5 One-sided Z-transform Inverse

10.6 State-Variable Representation

10.7 What have we accomplished? Where do we go from here?

10.8 Problems

11: Fourier Analysis of Discrete-time Signals and Systems

11.1 Introduction

11.2 The Discrete-Time Fourier Transform (DTFT)

11.3 Fourier Series of Discrete-Time Periodic Signals

11.4 The Discrete Fourier Transform (DFT)

11.5 What have we accomplished? Where do we go from here?

11.6 Problems

12: Introduction to the Design of Discrete Filters

12.1 Introduction

12.2 Frequency Selective Discrete Filters

12.3 Filter Specifications

12.4 IIR Filter Design

12.5 FIR Filter Design

12.6 Realization of Discrete Filters

12.7 What Have We Accomplished? Where Do We Go From Here?

12.8 Problems

Appendix: Useful Formulas

Bibliography

Index