# Fundamentals of Signals and Systems Using the Web and MATLAB,3rd edition

• Edward W. Kamen Georgia Institute of Technology (emeritus)
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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 MATLABÃ¢ 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.

â€¢ Extensive use of online demos â€“ Utilizes demos for data analysis to allow students to view results firsthand.

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

â€¢Â Wide range of examples and problems on different areas in engineering â€“ Touches on areas from electrical circuits and mechanical systems to electromechanical devices, such as a dc motor.

â€¢ Chapters on feedback control, digital filtering, and state representation â€“ Prepare students for senior electives in these topics.Â

â€¢Â Time-domain aspects of signals and systems (Chs. 1 and 2) â€“ 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.

â€¢Â Frequency-domain aspects of signals and systems â€“Â 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.

â€¢ Fourier analysis of discrete-time signals â€“ Focuses on the discrete-time Fourier transform (DTFT) and the discrete Fourier transform (DFT).

â€¢ Fourier theory applied to the study of both continuous-time and discrete-time systems â€“ Reviews applications to ideal analog filtering, sampling, signal reconstruction, and digital filtering.Â

â€¢Â Study of the Laplace transform â€“ Begins with the definition and properties, as well the transfer function representation of linear time-invariant continuous-time systems.

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

â€¢ Analysis of linear time-invariant continuous-time systems â€“ Uses the transfer function representation to carry out this analysis.

â€¢Â Transfer function framework â€“Â Applied to the problem of control (Ch. 9).

â€¢Â Laplace and z-transform frameworks â€“ Applied to the design of digital filters and controllers (Ch. 10).

â€¢ Fundamentals of the state description of linear time-invariant continuous-time and discrete-time systems â€“ Discussed in Ch.11.

â€¢Â Completely updated Companion Web-site (http://users.ece.gatech.edu/~bonnie/book3)Â  â€”Â 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.

â€¢ Substantially revised material on signals â€” 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.

â€¢ New section with examples of Fourier transforms â€”Â Illustrates the spectral content of common types of signals.

â€¢ Significantly restructured for greater usability â€”Â Reduces the degree of mathematical complexity and includes new practical applications involving downloaded data and other illustrations.

â€¢Â New illustrations and end-of-chapter summaries â€”Â Give additional insight into the meaning and significance of the mathematical formulations and material covered in each chapter.

â€¢Â Flexible organization of content â€” Allows instructors to adapt the presentation for use in either a one-quarter or one-semester course.

â€¢Â Focus on the problem of data analysis in the presence of noise â€” Addresses the issue of noise, which often arises in engineering, business, finance, and other fields.Â

â€¢Â Major enhancement of the MATLAB component â€” 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.

â€¢Â Enhanced material on control systems â€” Includes the description of a digital control lab project based on a LEGOÃ¢ Mindstorm kit, which provides students with hands-on experience in designing and implementing digital controllers for a dc motor.

PrefaceÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

1Â Â Â Â Â Â Â Â Â  FUNDAMENTAL CONCEPTSÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

1.1Â Â Â Â Continuous-Time Signals

1.2Â Â Â Â Discrete-Time Signals

1.3Â Â Â Â Systems

1.4Â Â Â Â Examples of SystemsÂ Â

1.5Â Â Â Â Basic System PropertiesÂ Â

Â Â Â Â Â Â Â Â  1.6 Â Â Â  Chapter Summary

ProblemsÂ Â

2Â Â Â Â Â Â Â Â Â  TIME-DOMAIN MODELS OF SYSTEMSÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

2.1Â Â Â Â Input/Output Representation of Discrete-Time Systems

2.2Â Â Â Â Convolution of Discrete-Time Signals

2.3Â Â Â Â Difference Equation Models

2.4Â Â Â Â Differential Equation Models

2.5Â Â Â Â Solution of Differential Equations

2.6 Â Â  Convolution Representation of Continuous-Time Systems

Â Â Â Â Â Â Â Â Â Â Â  2.7 Â Â Â  Chapter Summary

Â Â Â Â Â Â Â Â Â Â  Â Problems

3Â Â Â Â Â Â Â Â Â  THE FOURIER SERIES AND FOURIER TRANSFORMÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

3.1Â Â Â Â Representation of Signals in Terms of Frequency ComponentsÂ Â

3.2Â Â Â Â Trigonometric Fourier Series

3.3Â Â Â Â Complex Exponential Series

3.4Â Â Â  Fourier Transform

3.5Â Â Â  Spectral Content of Common Signals

3.6Â Â Â Â Properties of the Fourier TransformÂ Â

3.7Â Â Â Â Generalized Fourier TransformÂ Â

3.8Â Â Â  Application to Signal Modulation and Demodulation

Â Â Â Â Â Â Â Â Â Â Â  Â 3.9 Â Â  Â Chapter Summary

ProblemsÂ Â

4Â Â Â Â Â Â Â Â Â  FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS

4.1Â Â Â Â Â  Discrete-Time Fourier Transform

4.2Â Â Â Â Â  Discrete Fourier Transform

4.3Â Â Â Â Â  DFT of Truncated Signals

4.4Â Â Â Â Â  FFT Algorithm

4.5Â Â Â Â Â  Application to Data Analysis

Â Â Â Â Â Â Â Â Â Â Â  Â 4.6 Â Â Â Â  Chapter Summary

Â Problems

5Â Â Â Â Â Â Â Â Â  FOURIER ANALYSIS OF SYSTEMSÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

5.1Â Â Â Â Fourier Analysis of Continuous-Time Systems

5.2Â Â Â Â Response to Periodic and Nonperiodic InputsÂ Â

5.3Â Â Â Â Analysis of Ideal FiltersÂ Â

5.4Â Â Â Â SamplingÂ Â

5.5Â Â Â  Fourier Analysis of Discrete-Time Systems

5.6Â Â Â  Application to Lowpass Digital Filtering

Â Â Â Â Â Â Â Â Â Â Â  Â 5.7 Â Â  Â Chapter Summary

ProblemsÂ Â

6Â Â Â Â Â Â Â Â Â  THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATIONÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

6.1Â Â Â Â Laplace Transform of a SignalÂ Â

6.2Â Â Â Â Properties of the Laplace TransformÂ Â

6.3Â Â Â Â Computation of the Inverse Laplace TransformÂ Â

6.4Â Â Â Â Transform of the Input/Output Differential EquationÂ Â

6.5Â Â Â Â Transform of the Input/Output Convolution Integral

6.6Â Â Â Â Direct Construction of the Transfer Function

Â Â Â Â Â Â Â Â Â Â Â  6.7 Â Â Â  Chapter Summary

ProblemsÂ Â

7Â Â Â Â Â Â Â Â Â  THE z-TRANSFORM AND DISCRETE-TIME SYSTEMS

7.1Â Â Â z-Transform of a Discrete-Time SignalÂ Â

7.2Â Â Â Properties of the z-TransformÂ Â

7.3Â Â Â Computation of the Inverse z-TransformÂ Â

7.4Â Â Â Transfer Function RepresentationÂ Â

7.5Â Â Â  System Analysis Using the Transfer Function Representation

Â Â Â Â Â Â Â Â Â Â Â  Â 7.6 Â Â  Chapter Summary

Â Â Â Â Â Â Â Â Â Â Â Â  Problems

8Â Â Â Â Â Â Â Â Â  ANALYSIS OF CONTINUOUS-TIME SYSTEMS USING THE TRANSFER FUNCTION REPRESENTATIONÂ Â Â Â Â Â Â Â Â Â

8.1Â Â Â Â Stability and the Impulse ResponseÂ Â

8.2Â Â Â Â Routhâ€”Hurwitz Stability TestÂ Â

8.3Â Â Â Â Analysis of the Step ResponseÂ Â

8.4Â Â Â Â Response to Sinusoids and Arbitrary InputsÂ Â

8.5Â Â Â Â Frequency Response FunctionÂ Â

8.6Â Â Â Â Causal FiltersÂ Â

Â Â Â Â Â Â Â Â Â Â Â  Â 8.7 Â Â  Chapter Summary

ProblemsÂ Â

9Â Â Â Â Â Â Â Â Â  APPLICATION TO CONTROLÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

9.1Â Â Â Introduction to ControlÂ Â

9.2Â Â Â Tracking ControlÂ Â

9.3Â Â Â Root LocusÂ Â

9.4Â Â Â Application to Control System DesignÂ Â

Â Â Â Â Â Â Â Â  Â 9.5 Â Â  Chapter Summary

Â Â Â Â Â Â Â Â Â Â  Problems

10Â Â Â Â Â Â Â  DESIGN OF DIGITAL FILTERS AND CONTROLLERSÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

10.1Â Â Â DiscretizationÂ Â

10.2Â Â Â Design of IIR FiltersÂ Â

10.3Â Â Â Design of IIR Filters Using MATLABÂ Â

10.4Â Â Â Design of FIR FiltersÂ Â

10.5Â Â Â Design of Digital ControllersÂ Â

Â Â Â Â Â Â Â Â  Â 10.6 Â Â  Chapter Summary

ProblemsÂ Â

11Â Â Â Â Â Â Â  STATE REPRESENTATIONÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

11.1Â Â Â State ModelÂ Â

11.2Â Â Â Construction of State ModelsÂ Â

11.3Â Â Â Solution of State equationsÂ Â

11.4Â Â Â Discrete-Time SystemsÂ Â

11.5Â Â Â Equivalent State RepresentationsÂ Â

11.6Â Â Â Discretization of State ModelÂ Â

Â Â Â Â Â  Â Â Â  11.7 Â Â  Chapter Summary

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Problems

APPENDIX Â AÂ Â  BRIEF REVIEW OF COMPLEX VARIABLES

APPENDIXÂ Â BÂ Â  BRIEF REVIEW OF MATRICESÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

BIBLIOGRAPHYÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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