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Signals and Systems - Electrical Engineering

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  • Part 1 Introduction ACKNOWLEDGMENTS xvi

  • CHAPTER 0 From the Ground Up!.............................................................................

    • 0.1 Signals and Systems and Digital Technologies

    • 0.2 Examples of Signal Processing Applications

      • 0.2.1 Compact-Disc Player

      • 0.2.2 Software-Defined Radio and Cognitive Radio...............................

      • 0.2.3 Computer-Controlled Systems



    • 0.3 Analog or Discrete?

      • 0.3.1 Continuous-Time and Discrete-Time Representations

      • 0.3.2 Derivatives and Finite Differences

      • 0.3.3 Integrals and Summations.........................................................

      • 0.3.4 Differential and Difference Equations



    • 0.4 Complex or Real?

      • 0.4.1 Complex Numbers and Vectors

      • 0.4.2 Functions of a Complex Variable

      • 0.4.3 Phasors and Sinusoidal Steady State

      • 0.4.4 Phasor Connection



    • 0.5 Soft Introduction to MATLAB

      • 0.5.1 Numerical Computations

      • 0.5.2 Symbolic Computations

      • Problems............................................................................................



    • Signals and Systems Part 2 Theory and Application of Continuous-Time



  • CHAPTER 1 Continuous-Time Signals.........................................................................

    • 1.1 Introduction

    • 1.2 Classification of Time-Dependent Signals...............................................

    • 1.3 Continuous-Time Signals Contents v

      • 1.3.1 Basic Signal Operations—Time Shifting and Reversal

      • 1.3.2 Even and Odd Signals

      • 1.3.3 Periodic and Aperiodic Signals

      • 1.3.4 Finite-Energy and Finite Power Signals



    • 1.4 Representation Using Basic Signals.......................................................

      • 1.4.1 Complex Exponentials

      • 1.4.2 Unit-Step, Unit-Impulse, and Ramp Signals

      • 1.4.3 Special Signals—the Sampling Signal and the Sinc

        • and Windowing 1.4.4 Basic Signal Operations—Time Scaling, Frequency Shifting,



      • 1.4.5 Generic Representation of Signals..............................................



    • 1.5 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 2 Continuous-Time Systems.......................................................................

    • 2.1 Introduction

    • 2.2 System Concept

      • 2.2.1 System Classification................................................................



    • 2.3 LTI Continuous-Time Systems

      • 2.3.1 Linearity

      • 2.3.2 Time Invariance

      • 2.3.3 Representation of Systems by Differential Equations

      • 2.3.4 Application of Superposition and Time Invariance

      • 2.3.5 Convolution Integral.................................................................

      • 2.3.6 Causality

      • 2.3.7 Graphical Computation of Convolution Integral

      • 2.3.8 Interconnection of Systems—Block Diagrams

      • 2.3.9 Bounded-Input Bounded-Output Stability



    • 2.4 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 3 The Laplace Transform............................................................................

    • 3.1 Introduction

    • 3.2 The Two-Sided Laplace Transform

      • 3.2.1 Eigenfunctions of LTI Systems

      • 3.2.2 Poles and Zeros and Region of Convergence



    • 3.3 The One-Sided Laplace Transform

      • 3.3.1 Linearity

      • 3.3.2 Differentiation

      • 3.3.3 Integration

      • 3.3.4 Time Shifting...........................................................................

      • 3.3.5 Convolution Integral.................................................................



    • 3.4 Inverse Laplace Transform vi Contents

      • 3.4.1 Inverse of One-Sided Laplace Transforms

      • 3.4.2 Inverse of Functions Containinge−ρsTerms

      • 3.4.3 Inverse of Two-Sided Laplace Transforms



    • 3.5 Analysis of LTI Systems

      • 3.5.1 LTI Systems Represented by Ordinary Differential Equations

      • 3.5.2 Computation of the Convolution Integral



    • 3.6 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 4 Frequency Analysis: The Fourier Series..................................................

    • 4.1 Introduction

    • 4.2 Eigenfunctions Revisited

    • 4.3 Complex Exponential Fourier Series

    • 4.4 Line Spectra

      • 4.4.1 Parseval’s Theorem—Power Distribution over Frequency

      • 4.4.2 Symmetry of Line Spectra



    • 4.5 Trigonometric Fourier Series

    • 4.6 Fourier Coefficients from Laplace

    • 4.7 Convergence of the Fourier Series

    • 4.8 Time and Frequency Shifting................................................................

    • 4.9 Response of LTI Systems to Periodic Signals...........................................

      • 4.9.1 Sinusoidal Steady State.............................................................

      • 4.9.2 Filtering of Periodic Signals



    • 4.10 Other Properties of the Fourier Series

      • 4.10.1 Reflection and Even and Odd Periodic Signals

      • 4.10.2 Linearity of Fourier Series—Addition of Periodic Signals

      • 4.10.3 Multiplication of Periodic Signals

      • 4.10.4 Derivatives and Integrals of Periodic Signals



    • 4.11 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 5 Frequency Analysis: The Fourier Transform...........................................

    • 5.1 Introduction

    • 5.2 From the Fourier Series to the Fourier Transform

    • 5.3 Existence of the Fourier Transform

    • 5.4 Fourier Transforms from the Laplace Transform

    • 5.5 Linearity, Inverse Proportionality, and Duality

      • 5.5.1 Linearity

      • 5.5.2 Inverse Proportionality of Time and Frequency

      • 5.5.3 Duality

      • 5.6 Spectral Representation Contents vii

        • 5.6.1 Signal Modulation

        • 5.6.2 Fourier Transform of Periodic Signals

        • 5.6.3 Parseval’s Energy Conservation

        • 5.6.4 Symmetry of Spectral Representations........................................



      • 5.7 Convolution and Filtering.....................................................................

        • 5.7.1 Basics of Filtering

        • 5.7.2 Ideal Filters

        • 5.7.3 Frequency Response from Poles and Zeros..................................

        • 5.7.4 Spectrum Analyzer...................................................................



      • 5.8 Additional Properties

        • 5.8.1 Time Shifting

        • 5.8.2 Differentiation and Integration



      • 5.9 What Have We Accomplished? What Is Next?

        • Problems............................................................................................







  • CHAPTER 6 Application to Control and Communications...........................................

    • 6.1 Introduction

    • 6.2 System Connections and Block Diagrams

    • 6.3 Application to Classic Control...............................................................

      • 6.3.1 Stability and Stabilization

      • 6.3.2 Transient Analysis of First- and Second-Order Control Systems



    • 6.4 Application to Communications

      • 6.4.1 AM with Suppressed Carrier

      • 6.4.2 Commercial AM

      • 6.4.3 AM Single Sideband

      • 6.4.4 Quadrature AM and Frequency-Division Multiplexing

      • 6.4.5 Angle Modulation



    • 6.5 Analog Filtering

      • 6.5.1 Filtering Basics

      • 6.5.2 Butterworth Low-Pass Filter Design

      • 6.5.3 Chebyshev Low-Pass Filter Design

      • 6.5.4 Frequency Transformations

      • 6.5.5 Filter Design with MATLAB



    • 6.6 What Have We Accomplished? What Is Next?

      • Problems............................................................................................



    • Signals and Systems Part 3 Theory and Application of Discrete-Time



  • CHAPTER 7 Sampling Theory......................................................................................

    • 7.1 Introduction

    • 7.2 Uniform Sampling viii Contents

      • 7.2.1 Pulse Amplitude Modulation

      • 7.2.2 Ideal Impulse Sampling

      • 7.2.3 Reconstruction of the Original Continuous-Time Signal

      • 7.2.4 Signal Reconstruction from Sinc Interpolation..............................

      • 7.2.5 Sampling Simulation with MATLAB



    • 7.3 The Nyquist-Shannon Sampling Theorem

      • 7.3.1 Sampling of Modulated Signals



    • 7.4 Practical Aspects of Sampling

      • 7.4.1 Sample-and-Hold Sampling

      • 7.4.2 Quantization and Coding

      • 7.4.3 Sampling, Quantizing, and Coding with MATLAB



    • 7.5 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 8 Discrete-Time Signals and Systems.........................................................

    • 8.1 Introduction.....................................................................................

    • 8.2 Discrete-Time Signals

      • 8.2.1 Periodic and Aperiodic Signals

      • 8.2.2 Finite-Energy and Finite-Power Discrete-Time Signals

      • 8.2.3 Even and Odd Signals

      • 8.2.4 Basic Discrete-Time Signals



    • 8.3 Discrete-Time Systems

      • 8.3.1 Recursive and Nonrecursive Discrete-Time Systems.....................

        • Equations 8.3.2 Discrete-Time Systems Represented by Difference



      • 8.3.3 The Convolution Sum

      • 8.3.4 Linear and Nonlinear Filtering with MATLAB..............................

      • 8.3.5 Causality and Stability of Discrete-Time Systems



    • 8.4 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 9 The Z-Transform......................................................................................

    • 9.1 Introduction

    • 9.2 Laplace Transform of Sampled Signals...................................................

    • 9.3 Two-Sided Z-Transform

      • 9.3.1 Region of Convergence



    • 9.4 One-Sided Z-Transform........................................................................

      • 9.4.1 Computing the Z-Transform with Symbolic MATLAB

      • 9.4.2 Signal Behavior and Poles

      • 9.4.3 Convolution Sum and Transfer Function

      • 9.4.4 Interconnection of Discrete-Time Systems................................... Contents ix

      • 9.4.5 Initial and Final Value Properties



    • 9.5 One-Sided Z-Transform Inverse

      • 9.5.1 Long-Division Method

      • 9.5.2 Partial Fraction Expansion

      • 9.5.3 Inverse Z-Transform with MATLAB............................................

      • 9.5.4 Solution of Difference Equations

      • 9.5.5 Inverse of Two-Sided Z-Transforms



    • 9.6 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 10 Fourier Analysis of Discrete-Time Signals and Systems...........................

    • 10.1 Introduction

    • 10.2 Discrete-Time Fourier Transform

      • 10.2.1 Sampling, Z-Transform, Eigenfunctions, and the DTFT

      • 10.2.2 Duality in Time and Frequency

      • 10.2.3 Computation of the DTFT Using MATLAB

      • 10.2.4 Time and Frequency Supports

      • 10.2.5 Parseval’s Energy Result...........................................................

      • 10.2.6 Time and Frequency Shifts........................................................

      • 10.2.7 Symmetry

      • 10.2.8 Convolution Sum



    • 10.3 Fourier Series of Discrete-Time Periodic Signals......................................

      • 10.3.1 Complex Exponential Discrete Fourier Series

      • 10.3.2 Connection with the Z-Transform

      • 10.3.3 DTFT of Periodic Signals

      • 10.3.4 Response of LTI Systems to Periodic Signals

      • 10.3.5 Circular Shifting and Periodic Convolution



    • 10.4 Discrete Fourier Transform

      • 10.4.1 DFT of Periodic Discrete-Time Signals

      • 10.4.2 DFT of Aperiodic Discrete-Time Signals

      • 10.4.3 Computation of the DFT via the FFT

      • 10.4.4 Linear and Circular Convolution Sums



    • 10.5 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 11 Introduction to the Design of Discrete Filters..........................................

    • 11.1 Introduction

    • 11.2 Frequency-Selective Discrete Filters

      • 11.2.1 Linear Phase

      • 11.2.2 IIR and FIR Discrete Filters



    • 11.3 Filter Specifications x Contents

      • 11.3.1 Frequency-Domain Specifications

      • 11.3.2 Time-Domain Specifications



    • 11.4 IIR Filter Design

      • 11.4.1 Transformation Design of IIR Discrete Filters

      • 11.4.2 Design of Butterworth Low-Pass Discrete Filters

      • 11.4.3 Design of Chebyshev Low-Pass Discrete Filters

      • 11.4.4 Rational Frequency Transformations

      • 11.4.5 General IIR Filter Design with MATLAB



    • 11.5 FIR Filter Design

      • 11.5.1 Window Design Method

      • 11.5.2 Window Functions



    • 11.6 Realization of Discrete Filters

      • 11.6.1 Realization of IIR Filters

      • 11.6.2 Realization of FIR Filters



    • 11.7 What Have We Accomplished? Where Do We Go from Here?....................

      • Problems............................................................................................





  • CHAPTER 12 Applications of Discrete-Time Signals and Systems.................................

    • 12.1 Introduction

    • 12.2 Application to Digital Signal Processing

      • 12.2.1 Fast Fourier Transform

      • 12.2.2 Computation of the Inverse DFT

      • 12.2.3 General Approach of FFT Algorithms



    • 12.3 Application to Sampled-Data and Digital Control Systems

      • 12.3.1 Open-Loop Sampled-Data System

      • 12.3.2 Closed-Loop Sampled-Data System



    • 12.4 Application to Digital Communications

      • 12.4.1 Pulse Code Modulation

      • 12.4.2 Time-Division Multiplexing

        • Multiplexing............................................................................ 12.4.3 Spread Spectrum and Orthogonal Frequency-Division





    • 12.5 What Have We Accomplished? Where Do We Go from Here?....................



  • APPENDIX Useful Formulas.......................................................................................

  • BIBLIOGRAPHY

  • INDEX

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