The approach taken in Gopalan's text is to introduce students to the concepts and mathematical tools necessary to understand and appreciate the wide array of exciting fields in Electrical Engineering such as signal processing, control systems, and communications. The book is structured to introduce the basic continuous-time signal and system analysis concepts as an extension of familiar circuit analysis methods. A strong theoretical foundation for signal analysis is built, leading students to successfully discuss the various system analysis methods used in practice today. Use of MATLAB with appropriate examples has been integrated throughout the book.

### Table of Contents

1 - Introduction

1.1 Basic Definitions

1.2 Classification of Signals and Systems

1.3 Frequency spectrum in Signal and System Analysis

1.4 Scope of the Text

Summary

Further Reading

Problems

2 - Mathematical Modeling and Properties of Basic Signals and Systems

Introduction

2.1 Mathematical Modeling of Systems and Signals

2.2 Basic Signal Operations and Properties

2.3 Basic CT Signals

2.4 Basic DT Signals

2.5 Basic System Properties

2.6 Frequency Response and CT Filters

2.7 Discretization of CT Signal and System Models

2.8 Linearization of Nonlinear Systems

Summary

Key Equations

Further Reading

Problems

3 - Continuous-Time System Analysis in Time Domain

Introduction

3.1 Impulse-Response Characterization and the Convolution Integral for CT LTI Systems

3.2 Step and Other Causal Signal Responses of CT LTI Systems

3.3 Properties of Convolution

3.4 LTI System Properties from Impulse Response

3.5 Obtaining the Impulse Response of CT LTI Systems

3.6 System Analysis from a Linear Differential-Equation Model

3.7 CT System Response to Complex and Real Sinusoids and the system Function

3.8 Block Diagram Representation for System Simulation

Summary

Key Equations

Problems

4 - Discrete-Time System Analysis in the Time Domain - The Convolution Summation and Classical Analysis

Introduction

4.1 Impulse Response Characterization and the Convolution Summation

4.2 Step and Other Causal Signal Response of DT LTI Systems

4.3 Properties of the Convolution Summation

4.4 Obtaining the Impulse Response of DT LTI Systems

4.5 LTI System Properties from Impulse Response

4.6 System Analysis from the Difference-Equation Model

4.7 Forced Response to Complex and Real Sinusoids and the System Function

4.8 Block Diagram Representation for System Simulation

Summary

Key Equations

Further Reading

Problems

5 - Frequency Domain Analysis of CT Signals and Systems - The Fourier Series and the Fourier Transform Analysis

Introduction

5.1 Representation of Signals using Basic Functions

5.2 Representation of Periodic Functions - The Exponential Fourier Series

5.2.1 Existence of Fourier Series

5.2.2 Other Forms of Fourier Series

5.2.3 Frequency Spectrum of Periodic Signals

5.2.4 Fourier Series Properties

5.2.5 Fourier Series Representation of an Ideal Impulse Train

5.2.6 System Analysis for Nonsinusoidal Periodic Inputs

5.3 Frequency Spectrum of Aperiodic Signals - The Fourier Transform

5.3.1 Existence of Fourier Transform

5.3.2 Fourier Transform of Basic Signals

5.3.3 Fourier Transform Properties

5.4 LTI System Analysis in the Frequency Domain

5.5 Ideal and Practical Filters

Summary

Key Equations

Further Reading

Problems

6 - System Analysis Using the Laplace Transform

Introduction

6.1 The Bilateral and Unilateral Laplace Transforms

6.2 Laplace Transforms of Basic Signals

6.3 Laplace Transform Properties

6.4 Relationship between Fourier and Laplace Transforms

6.5 The Inverse Laplace Transform

6.6 Applications of the Laplace Transform in Solving Differential Equations

6.7 LTI System Transfer Functions

6.8 System Response and Stability from Transfer Functions

6.9 Step Response of Stable Systems

6.10 Sinusoidal Response of Stable Systems and the Frequency Response

6.11 Bode Plots

6.12 System Simulation

Summary

Key Equations

Further Reading

Problems

7 - The z Transform and Discrete-Time System Analysis

Introduction

7.1 The z-Transform

7.2 Convergence of the z-Transform

7.3 Basic z-Transforms

7.4 Properties of the z-Transform

7.4.1 Right and Left Shifted Signals

7.4.2 Multiplication by an Exponential Signal

7.4.3 Differentiation in the z-Domain

7.4.4 Accumulation

7.4.5 Convolution of Signals

7.4.6 Initial Value

7.4.7 Time Reversal

7.5 The Inverse z-Transform

7.5.1 Pole-Zero Plots and Inverse of Rational Functions of z

7.5.2 Inverse z-Transform from a Power Series Expansion

7.6 Solving Difference Equations using z-Transforms

7.7 DT LTI System Characterization

7.7.1 DT LTI System Transfer Functions from Impulse-Response Characterization

7.7.2 Transfer Functions from Difference-Equation Models

7.7.3 System Properties and Modes from H(z)

7.8 Frequency Response of DT Systems

7.9 Representation of Discrete-Time Systems for Implementation

7.10 The z-Transform of Sampled Signals - Relationship to the Laplace Transform

Summary

Key Equations

Further Reading

Problems

8 - Frequency Domain Analysis of DT Signals and Systems - The DTFT and DFT Analysis

Introduction

8.1 Spectrum of Sampled Signals and the Sampling Theorem

8.1.1 Aliasing

8.1.2 Signal Reconstruction

8.2 The Discrete-Time Fourier Transform

8.3 Properties of the Discrete-Time Fourier Transform

8.4 Frequency Domain Analysis of DT Systems

8.5 Discrete Fourier Transform and its Properties

8.6 Applications of the DFT in Signal and System Analysis

Summary

Key Equations

Further Reading

Problems

9 - State Variable Analysis of Continuous and Discrete-Time Systems

Introduction

9.1 State Variable Representation of CT Systems

9.1.1 Construction of State-Variable Models from System Configurations

9.1.2 Conversion of Differential-Equation Models to State-Variable Models

9.1.3 Obtaining State-Variable Models from Block Diagrams and Transfer Functions

9.1.4 System Analysis in Time and s-Domains Using State-Variable Models

9.1.5 MATLAB Applications

9.2 State Variable Representation and Analysis of DT Systems

9.2.1 Obtaining STate-Variable Models from Block Diagrams

9.2.2 Conversion of Transfer-Function and Difference-Equation Models to State-Variable Models

9.2.3 System Analysis in Time and z-Domains Using State Variable Models

9.2.4 MATLAB Applications

Summary

Key Equations

Further Reading

Problems

Appendix

A. Complex Numbers

B. Some Useful Mathematical Operations

C. Basic Matrix Operations

D. Mathematical Tables

Index