Description

For a one-quarter or one-semster course on Signals and Systems.

This new edition delivers an accessible yet comprehensive analytical introduction to continuous-time and discrete-time signals and systems. It also incorporates a strong emphasis on solving problems and exploring concepts, using demos, downloaded data, and MATLAB® to demonstrate solutions for a wide range of problems in engineering and other fields such as financial data analysis. Its flexible structure adapts easily for courses taught by semester or by quarter.

Features

• Extensive use of online demos – Utilizes demos for data analysis to allow students to view results firsthand.

• Use of MATLAB (Version 7.0) to generate computer implementations of the techniques for signal and system analysis and design – Gives students the opportunity to verify theories and experiment with applications of the techniques studied.

• Wide range of examples and problems on different areas in engineering – Touches on areas from electrical circuits and mechanical systems to electromechanical devices, such as a dc motor.

• Chapters on feedback control, digital filtering, and state representation – Prepare students for senior electives in these topics. 

• Time-domain aspects of signals and systems (Chs. 1 and 2) – Discusses the basic properties of signals and systems, the discrete-time convolution model, the input/output difference equation model, the input/output differential equation model, and the continuous-time convolution model.

• Frequency-domain aspects of signals and systems – Begins with signals that are a sum of sinusoids, then addresses the Fourier series representation of periodic signals, the Fourier transform of nonperiodic signals, and the use of the Fourier transform in the study of signal modulation.

• Fourier analysis of discrete-time signals – Focuses on the discrete-time Fourier transform (DTFT) and the discrete Fourier transform (DFT).

• Fourier theory applied to the study of both continuous-time and discrete-time systems – Reviews applications to ideal analog filtering, sampling, signal reconstruction, and digital filtering. 

• Study of the Laplace transform – Begins with the definition and properties, as well the transfer function representation of linear time-invariant continuous-time systems.

• Introduction of the z-transform and the transfer function representation of linear time-invariant discrete-time systems – Completes the discussion of the frequency response function first considered in Chapter 5.

• Analysis of linear time-invariant continuous-time systems – Uses the transfer function representation to carry out this analysis.

• Transfer function framework – Applied to the problem of control (Ch. 9).

• Laplace and z-transform frameworks – Applied to the design of digital filters and controllers (Ch. 10).

• Fundamentals of the state description of linear time-invariant continuous-time and discrete-time systems – Discussed in Ch.11.

New to this Edition

• Completely updated Companion Web-site (http://users.ece.gatech.edu/~bonnie/book3)  — Includes new and modified MATLAB M-files and data files used in the Third Edition, plus additional worked problems, on-line demos, and a MATLAB tutorial.

• Substantially revised material on signals — Discusses how to download signals (time series) from the Web and analyze the data; includes details on common types of digital filters, such as moving average and exponential moving average filters, with applications to filtering data downloaded from the Web; addresses signal analysis using the DFT to extract the dominant cyclic components of a signal.

• New section with examples of Fourier transforms — Illustrates the spectral content of common types of signals.

• Significantly restructured for greater usability — Reduces the degree of mathematical complexity and includes new practical applications involving downloaded data and other illustrations.

• New illustrations and end-of-chapter summaries — Give additional insight into the meaning and significance of the mathematical formulations and material covered in each chapter.

• Flexible organization of content — Allows instructors to adapt the presentation for use in either a one-quarter or one-semester course.

• Focus on the problem of data analysis in the presence of noise — Addresses the issue of noise, which often arises in engineering, business, finance, and other fields. 

• Major enhancement of the MATLAB component — Uses the MATLAB

Symbolic Math Toolbox throughout the text to complement and simplify various computational aspects of the theory and examples provided. Examples illustrate how this tool can be used to solve differential equations, evaluate integrals for computing system responses, and for computing Fourier and Laplace transforms, and inverse transforms, including inverse z-transforms.

• Enhanced material on control systems — Includes the description of a digital control lab project based on a LEGO® Mindstorm kit, which provides students with hands-on experience in designing and implementing digital controllers for a dc motor.

Table of Contents

Preface

1 FUNDAMENTAL CONCEPTS   

1.1  Continuous-Time Signals

1.2  Discrete-Time Signals

1.3  Systems

1.4  Examples of Systems  

1.5  Basic System Properties  

   1.6 Chapter Summary

Problems  

2 TIME-DOMAIN MODELS OF SYSTEMS  

2.1  Input/Output Representation of Discrete-Time Systems

2.2  Convolution of Discrete-Time Signals

2.3  Difference Equation Models

2.4  Differential Equation Models

2.5  Solution of Differential Equations

2.6    Convolution Representation of Continuous-Time Systems

   2.7 Chapter Summary

   Problems

3 THE FOURIER SERIES AND FOURIER TRANSFORM   

3.1  Representation of Signals in Terms of Frequency Components  

3.2  Trigonometric Fourier Series

3.3  Complex Exponential Series

3.4 Fourier Transform

3.5 Spectral Content of Common Signals

3.6  Properties of the Fourier Transform  

3.7  Generalized Fourier Transform  

3.8 Application to Signal Modulation and Demodulation

    3.9     Chapter Summary

Problems  

4 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS

4.1    Discrete-Time Fourier Transform

4.2    Discrete Fourier Transform

4.3    DFT of Truncated Signals

4.4    FFT Algorithm

4.5    Application to Data Analysis

    4.6   Chapter Summary

 Problems

5 FOURIER ANALYSIS OF SYSTEMS

5.1  Fourier Analysis of Continuous-Time Systems

5.2  Response to Periodic and Nonperiodic Inputs  

5.3  Analysis of Ideal Filters  

5.4  Sampling  

5.5 Fourier Analysis of Discrete-Time Systems

5.6 Application to Lowpass Digital Filtering

    5.7     Chapter Summary

Problems  

6 THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATION   

6.1  Laplace Transform of a Signal  

6.2  Properties of the Laplace Transform  

6.3  Computation of the Inverse Laplace Transform  

6.4  Transform of the Input/Output Differential Equation  

6.5  Transform of the Input/Output Convolution Integral

6.6  Direct Construction of the Transfer Function

   6.7 Chapter Summary

Problems  

7 THE z-TRANSFORM AND DISCRETE-TIME SYSTEMS

7.1 z-Transform of a Discrete-Time Signal  

7.2 Properties of the z-Transform  

7.3 Computation of the Inverse z-Transform  

7.4 Transfer Function Representation  

7.5 System Analysis Using the Transfer Function Representation

    7.6    Chapter Summary

Problems

8 ANALYSIS OF CONTINUOUS-TIME SYSTEMS USING THE TRANSFER FUNCTION REPRESENTATION  

8.1  Stability and the Impulse Response  

8.2  Routh—Hurwitz Stability Test  

8.3  Analysis of the Step Response  

8.4  Response to Sinusoids and Arbitrary Inputs  

8.5  Frequency Response Function  

8.6  Causal Filters  

    8.7    Chapter Summary

Problems  

9 APPLICATION TO CONTROL   

9.1 Introduction to Control  

9.2 Tracking Control  

9.3 Root Locus  

9.4 Application to Control System Design  

    9.5    Chapter Summary

  Problems

10   DESIGN OF DIGITAL FILTERS AND CONTROLLERS  

10.1 Discretization  

10.2 Design of IIR Filters  

10.3 Design of IIR Filters Using MATLAB  

10.4 Design of FIR Filters  

10.5 Design of Digital Controllers  

    10.6    Chapter Summary

Problems  

11   STATE REPRESENTATION   

11.1 State Model  

11.2 Construction of State Models  

11.3 Solution of State equations  

11.4 Discrete-Time Systems  

11.5 Equivalent State Representations  

11.6 Discretization of State Model  

   11.7    Chapter Summary

  Problems

APPENDIX  B   BRIEF REVIEW OF MATRICES