## Signals and Systems with MATLAB Computing and Simulink Modeling, Fifth Edition | by Steven T. Karris | ISBN: 9781934404232 | Circuit Analysis with Laplace Transforms. Discrete Fourier Transform (DFT). Analog and Digital Filters

**by Steven T. Karris
2012
ISBN: 9781934404232 **

Containing information on window functions, cross correlation and autocorrelation functions, a discussion on nonlinear systems, as well as additional end-of-chapter exercises, this text introduces signal and system analysis, digital signal processing, and the design of analog and digital filters.

[mp-amz keywords=”1934404233″]

**Table of Contents **

Signals and Systems with MATLAB Computing and Simulin Modeling, Fifth Edition

Preface

Chapter 1 – Elementary Signals

1.1: Signals Described in Math Form

1.2: The Unit Step Function u0(t)

1.3: The Unit Ramp Function u1(t)

1.4: The Delta Function d(t)

1.5: Higher Order Delta Functions

1.6: Summary

1.7: End-of-Chapter Exercises and Solutions

Chapter 2 – The Laplace Transformation

2.1: Definition of the Laplace Transformation

2.2: Properties and Theorems of the Laplace Transform

2.3: Laplace Transforms of Common Functions of Time

2.4: Laplace Transform of Common Waveforms

2.5: Using MATLAB for Finding the Laplace Transforms of Time Functions

2.6: Summary

2.7: End-of-Chapter Exercises and Solutions

Chapter 3 – The Inverse Laplace Transformation

3.1: The Inverse Laplace Transform Integral

3.2: Partial Fraction Expansion

3.3: Case where F(s) is Improper Rational Function

3.4: Alternate Method of Partial Fraction Expansion

3.5: Summary

3.6: End-of-Chapter Exercises and Solutions

Chapter 4 – Circuit Analysis with Laplace Transforms

4.1: Circuit Transformation from Time to Complex Frequency

4.2: Complex Impedance Z(s)

4.3: Complex Admittance Y(s)

4.4: Transfer Functions

4.5: Using the Simulink Transfer Fcn Block

4.6: Summary

4.7: End-of-Chapter Exercises and Solutions

Chapter 5 – State Variables and State Equations

5.1: Expressing Differential Equations in State Equation Form

5.2: Solution of Single State Equations

5.3: The State Transition Matrix

5.4: Computation of the State Transition Matrix eAt

5.5: Eigenvectors

5.6: Circuit Analysis with State Variables

5.7: Relationship between State Equations and Laplace Transform

5.8: Summary

5.9: End-of-Chapter Exercises and Solutions

Chapter 6 – The Impulse Response and Convolution

6.1: The Impulse Response in Time Domain

6.2: Even and Odd Functions of Time

6.3: Convolution

6.4: Graphical Evaluation of the Convolution Integral

6.5: Circuit Analysis with the Convolution Integral

6.6: Summary

6.7: End-of-Chapter Exercises and Solutions

Chapter 7 – Fourier Series

7.1: Wave Analysis

7.2: Evaluation of the Coefficients

7.3: Symmetry in Trigonometric Fourier Series

7.4: Trigonometric Form of Fourier Series for Common Waveforms

7.5: Gibbs Phenomenon

7.6: Alternate Forms of the Trigonometric Fourier Series

7.7: Circuit Analysis with Trigonometric Fourier Series

7.8: The Exponential Form of the Fourier Series

7.9: Symmetry in Exponential Fourier Series

7.10: Line Spectra

7.11: Computation of RMS Values from Fourier Series

7.12: Computation of Average Power from Fourier Series

7.13: Evaluation of Fourier Coefficients Using Excel®

7.14: Evaluation of Fourier Coefficients Using MATLAB®

7.15: Summary

7.16: Solutions to End?of?Chapter Exercises

Chapter 8 – The Fourier Transform

8.1: Definition and Special Forms

8.2: Special Forms of the Fourier Transform

8.3: Properties and Theorems of the Fourier Transform

8.4: Fourier Transform Pairs of Common Functions

8.5: Derivation of the Fourier Transform from the Laplace Transform

8.6: Fourier Transforms of Common Waveforms

8.7: Using MATLAB for Finding the Fourier Transform of Time Functions

8.8: The System Function and Applications to Circuit Analysis

8.9: Summary

8.10: End-of-Chapter Exercises and Solutions

Chapter 9 – Discrete-Time Systems and the Transform

9.1: Definition and Special Forms

9.2: Properties and Theorems of the Transform

9.3: The Transform of Common Discrete-Time Functions

9.4: Computation of the Transform with Contour Integration

9.5: Transformation Between s and z Domains

9.6: The Inverse Transform

9.7: The Transfer Function of Discrete-Time Systems

9.8: State Equations for Discrete-Time Systems

9.9: Summary

9.10: Solutions to End-of-Chapter Exercises

Chapter 10 – The DFT and the FFT Algorithm

10.1: The Discrete Fourier Transform (DFT)

10.2: Even and Odd Properties of the DFT

10.3: Common Properties and Theorems of the DFT

10.4: The Sampling Theorem

10.5: Number of Operations Required to Compute the DFT

The Fast Fourier Transform (FFT)

10.7: Summary

10.8: End-of-Chapter Exercises and Solutions

Chapter 11 – Analog and Digital Filters

11.1: Filter Types and Classifications

11.2: Basic Analog Filters

11.3: Low-Pass Analog Filter Prototypes

11.4: High–Pass, Band–Pass, and Band–Elimination Filter Design

11.5: Digital Filters

11.6: Digital Filter Design with Simulink

11.7: Summary

11.8: End-of-Chapter Exercises and Solutions

Appendix A – Introduction to MATLAB®

A.1: MATLAB® and Simulink®

A.2: Command Window

A.3: Roots of Polynomials

A.4: Polynomial Construction from Known Roots

A.5: Evaluation of a Polynomial at Specified Values

A.6: Rational Polynomials

A.7: Using MATLAB to Make Plots

A.8: Subplots

A.9: Multiplication, Division, and Exponentiation

A.10: Script and Function Files

A.11: Display Formats

Appendix B – Introduction to Simulink

B.1: Simulink and Its Relation to MATLAB

B.2: Simulink Demos

Appendix C – A Review of Complex Numbers

C.1: Definition of a Complex Number

C.2: Addition and Subtraction of Complex Numbers

C.3: Multiplication of Complex Numbers

C.4: Division of Complex Numbers

C.5: Exponential and Polar Forms of Complex Numbers

Appendix D – Matrices and Determinants

D.1: Matrix Definition

D.2: Matrix Operations

D.3: Special Forms of Matrices

D.4: Determinants

D.5: Minors and Cofactors

D.6: Cramer’s Rule

D.7: Gaussian Elimination Method

D.8: The Adjoint of a Matrix

D.9: Singular and Non-Singular Matrices

D.10: The Inverse of a Matrix

D.11: Solution of Simultaneous Equations with Matrices

Appendix E – Window Functions

E.1: Window Function Defined

E.2: Common Window Functions

E.3: Other Window Functions

E.4: Fourier Series Method for Approximating an FIR Amplitude Response

Appendix F – Correlation Functions

F.1: Cross Correlation

F.2: Autocorrelation

Appendix G – Nonlinear Systems

References and Suggestions for Further Study

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