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Signals, Systems, and Transforms, Coursesmart eTextbook, 4th Edition

By Charles Phillips, John M. Parr, Eve A. Riskin

Published by Prentice Hall

Published Date: Feb 12, 2008

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Description

For sophomore/junior-level signals and systems courses in Electrical and Computer Engineering departments.

 

This text provides a clear, comprehensive presentation of both the theory and applications in signals, systems, and transforms. It presents the mathematical background of signals and systems, including the Fourier transform, the Fourier series, the Laplace transform, the discrete-time and the discrete Fourier transforms, and the z-transform. The text integrates MATLAB examples into the presentation of signal and system theory and applications.

Table of Contents

Contents

Preface                                                                                                                                                                   

1          Introduction                                                                                                                                             

1.1        Modeling   

1.2        Continuous-Time Physical Systems   

Electric Circuits,   

Operational Amplifier Circuits,   

Simple Pendulum,  

DC Power Supplies,   

Analogous Systems,   

1.3        Samplers and Discrete-Time Physical Systems   

Analog-to-Digital Converter,   

Numerical Integration,   

Picture in a Picture,   

Compact Disks,   

Sampling in Telephone Systems,   

Data-Acquisition System,   

1.4        Matlab and Simulink   

2          Continuous-Time Signals and Systems                                                                                  

2.1        Transformations of Continuous-Time Signals   

Time Transformations,   

Amplitude Transformations,   

2.2        Signal Characteristics   

Even and Odd Signals,   

Periodic Signals,   

2.3        Common Signals in Engineering   

2.4        Singularity Functions   

Unit Step Function,   

Unit Impulse Function,   

2.5        Mathematical Functions for Signals   

2.6        Continuous-Time Systems   

Interconnecting Systems,   

Feedback System,   

2.7        Properties of Continuous-Time Systems   

Stability   

Linearity   

Summary   

Problems   

3          Continuous-Time Linear Time-Invariant Systems                                                           

3.1        Impulse Representation of Continuous-Time Signals  

3.2        Convolution for Continuous-Time LTI Systems  

3.3        Properties of Convolution   

3.4        Properties of Continuous-Time LTI Systems   

Memoryless Systems,   

Invertibility,   

Causality,   

Stability,   

Unit Step Response,   

3.5        Differential-Equation Models  

Solution of Differential Equations,   

General Case,   

Relation to Physical Systems,   

3.6        Terms in the Natural Response   

Stability,   

3.7        System Response for Complex-Exponential Inputs   

Linearity,   

Complex Inputs for LTI Systems,   

Impulse Response,   

3.8        Block Diagrams   

Direct Form I,   

Direct Form II,   

nth-Order Realizations,   

Practical Considerations,   

Summary   

Problems   

4          Fourier Series                                                                                                                                       

4.1        Approximating Periodic Functions   

Periodic Functions,   

Approximating Periodic Functions,   

4.2        Fourier Series   

Fourier Series,

Fourier Coefficients,   

4.3        Fourier Series and Frequency Spectra   

Frequency Spectra,   

4.4        Properties of Fourier Series   

4.5        System Analysis   

4.6        Fourier Series Transformations   

Amplitude Transformations,   

Time Transformations,   

Summary   

Problems   

5          The Fourier Transform                                                                                                                  

5.1        Definition of the Fourier Transform   

5.2        Properties of the Fourier Transform   

Linearity,   

Time Scaling,   

Time Shifting,   

Time Transformation,   

Duality,   

Convolution,   

Frequency Shifting,   

Time Differentiation,   

Time Integration,   

Frequency Differentiation,   

Summary,   

5.3        Fourier Transforms of Time Functions   

DC Level,   

Unit Step Function,   

Switched Cosine,   

Pulsed Cosine,   

Exponential Pulse,   

Fourier Transforms of Periodic Functions,   

Summary,   

5.4        Sampling Continuous-Time Signals   

Impulse Sampling,   

Shannon’s Sampling Theorem,   

Practical Sampling,   

5.5        Application of the Fourier Transform   

Frequency Response of Linear Systems,   

Frequency Spectra of Signals,   

Summary, 

5.6        Energy and Power Density Spectra   

Energy Density Spectrum,   

Power Density Spectrum,   

Power and Energy Transmission,   

Summary,   

Summary   

Problems   

6          Applications of the Fourier Transform                                                                           

6.1        Ideal Filters   

6.2        Real Filters   

RC Low-Pass Filter,   

Butterworth Filter,   

Chebyschev and Elliptic Filters,   

Bandpass Filters,   

Summary,   

6.3        Bandwidth Relationships   

6.4        Reconstruction of signals from sample data   

Interpolating Function,   

Digital-to-analog Conversion,   

6.5        Sinusoidal Amplitude Modulation   

Frequency-Division Multiplexing,   

6.6        Pulse-Amplitude Modulation   

Time-Division Multiplexing,   

Flat-Top PAM,   

Summary   

Problems   

7          The Laplace Transform                                                                                                                

7.1        Definitions of Laplace Transforms   

7.2        Examples   

7.3        Laplace Transforms of Functions   

7.4        Laplace Transform Properties   

Real Shifting,  

Differentiation,   

Integration,   

7.5        Additional Properties   

Multiplication by t,   

Initial Value,   

Final Value,   

Time Transformation,   

7.6        Response of LTI Systems   

Initial Conditions,   

Transfer Functions,   

Convolution,   

Transforms with Complex Poles,   

Functions with Repeated Poles,   

7.7        LTI Systems Characteristics   

Causality,   

Stability,   

Invertibility,  

Frequency Response,   

7.8        Bilateral Laplace Transform   

Region of Convergence,   

Bilateral Transform from Unilateral Tables,   

Inverse Bilateral Laplace Transform,   

7.9        Relationship of the Laplace Transform to the Fourier Transform 

Summary   

Problems   

8          State Variables for Continuous-Time Systems                                                            

8.1        State-Variable Modeling   

8.2        Simulation Diagrams   

8.3        Solution of State Equations   

Laplace-Transform Solution,   

Convolution Solution,   

Infinite Series Solution,  

8.4        Properties of the State Transition Matrix   

8.5        Transfer Functions   

Stability,   

8.6        Similarity Transformations   

Transformations,   

Properties,   

Summary   

Problems   

9          Discrete-Time Signals and Systems                                                                                       

9.1        Discrete-Time Signals and Systems   

Unit Step and Unit Impulse Functions,   

Equivalent Operations,   

9.2        Transformations of Discrete-Time Signals   

Time Transformations,  

Amplitude Transformations,   

9.3        Characteristics of Discrete-Time Signals   

Even and Odd Signals, 

Signals Periodic in n,   

Signals Periodic in W   

9.4        Common Discrete-Time Signals   

9.5        Discrete-Time Systems   

Interconnecting Systems,   

9.6        Properties of Discrete-Time Systems   

Systems with Memory,   

Invertibility,   

Inverse of a System,   

Causality,   

Stability,   

Time Invariance,   

Linearity,   

Summary   

Problems   

10        Discrete-Time Linear Time-Invariant Systems                                                                

10.1      Impulse Representation of Discrete-Time Signals   

10.2      Convolution for Discrete-Time Systems   

Properties of Convolution,   

10.3      Properties of Discrete-Time LTI Systems   

Memory,   

Invertibility,   

Causality,   

Stability,   

Unit Step Response,   

10.4      Difference-Equation Models   

Difference-Equation Models,   

Classical Method,   

Solution by Iteration,   

10.5      Terms in the Natural Response   

Stability,   

10.6      Block Diagrams   

Two Standard Forms,   

10.7      System Response for Complex-Exponential Inputs   

Linearity,   

Complex Inputs for LTI Systems,   

Stability,   

Sampled Signals,   

Impulse Response,   

Summary   

Problems   

11        The z-Transform                                                                                                                                 

11.1      Definitions of z-Transforms   

11.2      Examples   

Two z-Transforms,   

Digital-Filter Example,   

11.3      z-Transforms of Functions   

Sinusoids,   

11.4      z-Transform Properties   

Real Shifting,   

Initial and Final Values,   

11.5      Additional Properties   

Time Scaling,   

Convolution in Time,   

11.6      LTI System Applications   

Transfer Functions,   

Inverse z-Transform,   

Complex Poles,   

Causality,   

Stability,   

Invertibility,   

11.7      Bilateral z-Transform   

Bilateral Transforms,   

Regions of Convergence,    

Inverse Bilateral Transforms,   

Summary   

Problems   

12        Fourier Transforms of Discrete-Time Signals                                                             

12.1      Discrete-Time Fourier Transform   

z-Transform,   

12.2      Properties of the Discrete-Time Fourier Transform   

Periodicity,   

Linearity,   

Time Shift,   

Frequency Shift,   

Symmetry,   

Time Reversal,   

Convolution in Time,   

Convolution in Frequency,   

Multiplication by n,   

Parseval’s Theorem,   

12.3      Discrete-Time Fourier Transform of Periodic Sequences   

12.4      Discrete Fourier Transform   

Shorthand Notation for the DFT,   

Frequency Resolution of the DFT,  

Validity of the DFT,   

Summary,   

12.5      Fast Fourier Transform   

Decomposition-in-Time Fast Fourier Transform Algorithm,   

Decomposition-in-Frequency Fast Fourier Transform,   

Summary,   

12.6      Applications of the Discrete Fourier Transform   

Calculation of Fourier Transforms,   

Convolution,   

Filtering,   

Correlation,   

Energy Spectral Density Estimation,   

Summary,   

12.7      The Discrete Cosine Transform,   

Summary   

Problems   

13        State Variables for Discrete-Time Systems                                                                   

13.1      State-Variable Modeling   

13.2      Simulation Diagrams   

13.3      Solution of State Equations   

Recursive Solution,   

z-Transform Solution,   

13.4      Properties of the State Transition Matrix   

13.5      Transfer Functions   

Stability,   

13.6      Similarity Transformations   

Properties,   

Summary   

Problems   

Appendices                                                                                                                                                           

A.        Integrals and Trigonometric Identities   

Integrals,  

Trigonometric Identities,   

B.         Leibnitz’s and L’Hôpital’s Rules   

Leibnitz’s Rule,   

L’Hôpital’s Rule,   

C.         Summation Formulas for Geometric Series   

D.         Complex Numbers and Euler’s Relation   

Complex-Number Arithmetic,   

Euler’s Relation,   

Conversion Between Forms,   

E.         Solution of Differential Equations   

Complementary Function,   

Particular Solution,   

General Solution,   

Repeated Roots,   

F.         Partial-Fraction Expansions   

G.         Review of Matrices   

Algebra of Matrices,   

Other Relationships   

H.         Answers to Selected Problems   

I.          Signals and Systems References   

Index                                                                                                                                                                        

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Signals, Systems, and Transforms, Coursesmart eTextbook, 4th Edition
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