Simon Haykin, PhD, is University Professor and Director of the Adaptive Systems Laboratory at McMaster University.Barry Van Veen, University of Wisconsin.

• Preface viiNotation xviiChapter 1 Introduction 11.1 What Is a Signal? 11.2 Classification of Signals 21.3 Basic Operations on Signals 111.4 Elementary Signals 191.5 What Is a System? 381.6 Overview of Specific Systems 391.7 Systems Viewed as Interconnections of Operations 521.8 Properties of Systems 541.9 Noise 681.10 Theme Examples 711.11 Exploring Concepts with MATLAB 801.12 Summary 86Further Reading 87Additional Problems 88Advanced Problems 94Computer Experiments 97Chapter 2 Time-Domain Representations of Linear Time-Invariant Systems 992.1 Introduction 992.2 The Convolution Sum 1002.3 Convolution Sum Evaluation Procedure 1042.4 The Convolution Integral 1182.5 Convolution Integral Evaluation Procedure 1202.6 Interconnections of LTI Systems 1322.7 Relations Between LTI System Properties and the Impulse Response 1382.8 Step Response 1442.9 Differential and Difference Equation Representations of LTI Systems 1462.10 Solving Differential and Difference Equations 1532.11 Characteristics of Systems Described by Differential and Difference Equations 1632.12 Block Diagram Representations 1692.13 State-Variable Descriptions of LTI Systems 1742.14 Exploring Concepts with MATLAB 1842.15 Summary 190Further Reading 191Additional Problems 192Advanced Problems 201Computer Experiments 203Chapter 3 Fourier Representations of Signals and Linear Time-Invariant Systems 2053.1 Introduction 2053.2 Complex Sinusoids and Frequency Response of LTI Systems 2063.3 Fourier Representations for Four Classes of Signals 2093.4 Discrete-Time Periodic Signals: The Discrete-Time Fourier Series 2123.5 Continuous-Time Periodic Signals: The Fourier Series 2253.6 Discrete-Time Nonperiodic Signals: The Discrete-Time Fourier Transform 2413.7 Continuous-Time Nonperiodic Signals: The Fourier Transform 2523.8 Properties of Fourier Representations 2653.9 Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions 3113.10 Parseval Relationships 3173.11 Time−Bandwidth Product 3193.12 Duality 3213.13 Exploring Concepts with MATLAB 3273.14 Summary 335Further Reading 336Additional Problems 337Advanced Problems 348Computer Experiments 353Chapter 4 Applications of Fourier Representations to Mixed Signal Classes 3574.1 Introduction 3574.2 Fourier Transform Representations of Periodic Signals 3584.3 Convolution and Multiplication with Mixtures of Periodic and Nonperiodic Signals 3644.4 Fourier Transform Representation of Discrete-Time Signals 3754.5 Sampling 3794.6 Reconstruction of Continuous-Time Signals from Samples 3884.7 Discrete-Time Processing of Continuous-Time Signals 4004.8 Fourier Series Representations of Finite-Duration Nonperiodic Signals 4074.9 The Discrete-Time Fourier Series Approximation to the Fourier Transform 4144.10 Efficient Algorithms for Evaluating the DTFS 4224.11 Exploring Concepts with MATLAB 4264.12 Summary 429Further Reading 430Additional Problems 431Advanced Problems 436Computer Experiments 440Chapter 5 The Laplace Transform 4435.1 Introduction 4435.2 The Laplace Transform 4435.3 The Unilateral Laplace Transform 4515.4 Properties of the Unilateral Laplace Transform 4525.5 Inversion of the Unilateral Laplace Transform 4575.6 Solving Differential Equations with Initial Conditions 4625.7 Laplace Transform Methods in Circuit Analysis 4675.8 Properties of the Bilateral Laplace Transform 4705.9 Properties of the Region of Convergence 4735.10 Inversion of the Bilateral Laplace Transform 4775.11 The Transfer Function 4815.12 Causality and Stability 4845.13 Determining the Frequency Response from Poles and Zeros 4895.14 Exploring Concepts with MATLAB 5025.15 Summary 505Further Reading 507Additional Problems 507Advanced Problems 511Computer Experiments 513Chapter 6 The z-Transform 5156.1 Introduction 5156.2 The z-Transform 5156.3 Properties of the Region of Convergence 5246.4 Properties of the z-Transform 5296.5 Inversion of the z-Transform 5356.6 The Transfer Function 5436.7 Causality and Stability 5476.8 Determining the Frequency Response from Poles and Zeros 5536.9 Computational Structures for Implementing Discrete-Time LTI Systems 5596.10 The Unilateral z-Transform 5626.11 Exploring Concepts with MATLAB 5686.12 Summary 571Further Reading 572Additional Problems 572Advanced Problems 576Computer Experiments 579Chapter 7 Application to Communication Systems 5817.1 Introduction 5817.2 Types of Modulation 5817.3 Benefits of Modulation 5857.4 Full Amplitude Modulation 5877.5 Double Sideband-Suppressed Carrier Modulation 5967.6 Quadrature-Carrier Multiplexing 6017.7 Other Variants of Amplitude Modulation 6027.8 Pulse-Amplitude Modulation 6077.9 Multiplexing 6117.10 Phase and Group Delays 6167.11 Exploring Concepts with MATLAB 6207.12 Summary 630Further Reading 631Additional Problems 632Advanced Problems 635Computer Experiments 637Chapter 8 Application to Filters and Equalizers 6398.1 Introduction 6398.2 Conditions for Distortionless Transmission 6398.3 Ideal Low-Pass Filters 6428.4 Design of Filters 6488.5 Approximating Functions 6498.6 Frequency Transformations 6568.7 Passive Filters 6588.8 Digital Filters 6598.9 FIR Digital Filters 6618.10 IIR Digital Filters 6708.11 Linear Distortion 6758.12 Equalization 6768.13 Exploring Concepts with MATLAB 6808.14 Summary 685Further Reading 685Additional Problems 686Advanced Problems 688Computer Experiments 689Chapter 9 Application to Linear Feedback Systems 6919.1 Introduction 6919.2 What Is Feedback? 6919.3 Basic Feedback Concepts 6939.4 Sensitivity Analysis 6969.5 Effect of Feedback on Disturbance or Noise 6989.6 Distortion Analysis 6999.7 Summarizing Remarks on Feedback 7019.8 Operational Amplifiers 7019.9 Control Systems 7079.10 Transient Response of Low-Order Systems 7109.11 The Stability Problem 7139.12 Routh–Hurwitz Criterion 7179.13 Root Locus Method 7219.14 Nyquist Stability Criterion 7309.15 Bode Diagram 7369.16 Sampled-Data Systems 7419.17 Exploring Concepts with MATLAB 7519.18 Summary 755Further Reading 756Additional Problems 757Advanced Problems 760Computer Experiments 765Chapter 10 Epilogue 76910.1 Introduction 76910.2 Speech Signals: An Example of Nonstationarity 77010.3 Time–Frequency Analysis 77110.4 Nonlinear Systems 78210.5 Adaptive Filters 78910.6 Concluding Remarks 792Further Reading 792Appendix A Selected Mathematical Identities 795A. 1 Trigonometry 795A. 2 Complex Numbers 796A. 3 Geometric Series 797A. 4 Definite Integrals 797A. 5 Matrices 798Appendix B Partial-Fraction Expansions 800B. 1 Partial-Fraction Expansions of Continuous-Time Representations 800B. 2 Partial-Fraction Expansions of Discrete-Time Representation 803Appendix C Tables of Fourier Representations and Properties 806C. 1 Basic Discrete-Time Fourier Series Pairs 806C. 2 Basic Fourier Series Pairs 807C. 3 Basic Discrete-Time Fourier Transform Pairs 807C. 4 Basic Fourier Transform Pairs 808C. 5 Fourier Transform Pairs for Periodic Signals 808C. 6 Discrete-Time Fourier Transform Pairs for Periodic Signals 809C. 7 Properties of Fourier Representations 810C. 8 Relating the Four Fourier Representations 812C. 9 Sampling and Aliasing Relationships 812Appendix D Tables of Laplace Transforms and Properties 814D. 1 Basic Laplace Transforms 814D. 2 Laplace Transform Properties 815Appendix E Tables of z-Transforms and Properties 817E.1 Basic z-Transforms 817E.2 z-Transform Properties 818Appendix F Introduction to MATLAB 819F. 1 Basic Arithmetic Rules 819F. 2 Variables and Variable Names 820F. 3 Vectors and Matrices 820F. 4 Plotting in MATLAB 823F. 5 M-files 824F. 6 Additional Help 825Index 827

Simon Haykin, PhD, is University Professor and Director of the Adaptive Systems Laboratory at McMaster University.Barry Van Veen, University of Wisconsin.

• Preface viiNotation xviiChapter 1 Introduction 11.1 What Is a Signal? 11.2 Classification of Signals 21.3 Basic Operations on Signals 111.4 Elementary Signals 191.5 What Is a System? 381.6 Overview of Specific Systems 391.7 Systems Viewed as Interconnections of Operations 521.8 Properties of Systems 541.9 Noise 681.10 Theme Examples 711.11 Exploring Concepts with MATLAB 801.12 Summary 86Further Reading 87Additional Problems 88Advanced Problems 94Computer Experiments 97Chapter 2 Time-Domain Representations of Linear Time-Invariant Systems 992.1 Introduction 992.2 The Convolution Sum 1002.3 Convolution Sum Evaluation Procedure 1042.4 The Convolution Integral 1182.5 Convolution Integral Evaluation Procedure 1202.6 Interconnections of LTI Systems 1322.7 Relations Between LTI System Properties and the Impulse Response 1382.8 Step Response 1442.9 Differential and Difference Equation Representations of LTI Systems 1462.10 Solving Differential and Difference Equations 1532.11 Characteristics of Systems Described by Differential and Difference Equations 1632.12 Block Diagram Representations 1692.13 State-Variable Descriptions of LTI Systems 1742.14 Exploring Concepts with MATLAB 1842.15 Summary 190Further Reading 191Additional Problems 192Advanced Problems 201Computer Experiments 203Chapter 3 Fourier Representations of Signals and Linear Time-Invariant Systems 2053.1 Introduction 2053.2 Complex Sinusoids and Frequency Response of LTI Systems 2063.3 Fourier Representations for Four Classes of Signals 2093.4 Discrete-Time Periodic Signals: The Discrete-Time Fourier Series 2123.5 Continuous-Time Periodic Signals: The Fourier Series 2253.6 Discrete-Time Nonperiodic Signals: The Discrete-Time Fourier Transform 2413.7 Continuous-Time Nonperiodic Signals: The Fourier Transform 2523.8 Properties of Fourier Representations 2653.9 Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions 3113.10 Parseval Relationships 3173.11 Time−Bandwidth Product 3193.12 Duality 3213.13 Exploring Concepts with MATLAB 3273.14 Summary 335Further Reading 336Additional Problems 337Advanced Problems 348Computer Experiments 353Chapter 4 Applications of Fourier Representations to Mixed Signal Classes 3574.1 Introduction 3574.2 Fourier Transform Representations of Periodic Signals 3584.3 Convolution and Multiplication with Mixtures of Periodic and Nonperiodic Signals 3644.4 Fourier Transform Representation of Discrete-Time Signals 3754.5 Sampling 3794.6 Reconstruction of Continuous-Time Signals from Samples 3884.7 Discrete-Time Processing of Continuous-Time Signals 4004.8 Fourier Series Representations of Finite-Duration Nonperiodic Signals 4074.9 The Discrete-Time Fourier Series Approximation to the Fourier Transform 4144.10 Efficient Algorithms for Evaluating the DTFS 4224.11 Exploring Concepts with MATLAB 4264.12 Summary 429Further Reading 430Additional Problems 431Advanced Problems 436Computer Experiments 440Chapter 5 The Laplace Transform 4435.1 Introduction 4435.2 The Laplace Transform 4435.3 The Unilateral Laplace Transform 4515.4 Properties of the Unilateral Laplace Transform 4525.5 Inversion of the Unilateral Laplace Transform 4575.6 Solving Differential Equations with Initial Conditions 4625.7 Laplace Transform Methods in Circuit Analysis 4675.8 Properties of the Bilateral Laplace Transform 4705.9 Properties of the Region of Convergence 4735.10 Inversion of the Bilateral Laplace Transform 4775.11 The Transfer Function 4815.12 Causality and Stability 4845.13 Determining the Frequency Response from Poles and Zeros 4895.14 Exploring Concepts with MATLAB 5025.15 Summary 505Further Reading 507Additional Problems 507Advanced Problems 511Computer Experiments 513Chapter 6 The z-Transform 5156.1 Introduction 5156.2 The z-Transform 5156.3 Properties of the Region of Convergence 5246.4 Properties of the z-Transform 5296.5 Inversion of the z-Transform 5356.6 The Transfer Function 5436.7 Causality and Stability 5476.8 Determining the Frequency Response from Poles and Zeros 5536.9 Computational Structures for Implementing Discrete-Time LTI Systems 5596.10 The Unilateral z-Transform 5626.11 Exploring Concepts with MATLAB 5686.12 Summary 571Further Reading 572Additional Problems 572Advanced Problems 576Computer Experiments 579Chapter 7 Application to Communication Systems 5817.1 Introduction 5817.2 Types of Modulation 5817.3 Benefits of Modulation 5857.4 Full Amplitude Modulation 5877.5 Double Sideband-Suppressed Carrier Modulation 5967.6 Quadrature-Carrier Multiplexing 6017.7 Other Variants of Amplitude Modulation 6027.8 Pulse-Amplitude Modulation 6077.9 Multiplexing 6117.10 Phase and Group Delays 6167.11 Exploring Concepts with MATLAB 6207.12 Summary 630Further Reading 631Additional Problems 632Advanced Problems 635Computer Experiments 637Chapter 8 Application to Filters and Equalizers 6398.1 Introduction 6398.2 Conditions for Distortionless Transmission 6398.3 Ideal Low-Pass Filters 6428.4 Design of Filters 6488.5 Approximating Functions 6498.6 Frequency Transformations 6568.7 Passive Filters 6588.8 Digital Filters 6598.9 FIR Digital Filters 6618.10 IIR Digital Filters 6708.11 Linear Distortion 6758.12 Equalization 6768.13 Exploring Concepts with MATLAB 6808.14 Summary 685Further Reading 685Additional Problems 686Advanced Problems 688Computer Experiments 689Chapter 9 Application to Linear Feedback Systems 6919.1 Introduction 6919.2 What Is Feedback? 6919.3 Basic Feedback Concepts 6939.4 Sensitivity Analysis 6969.5 Effect of Feedback on Disturbance or Noise 6989.6 Distortion Analysis 6999.7 Summarizing Remarks on Feedback 7019.8 Operational Amplifiers 7019.9 Control Systems 7079.10 Transient Response of Low-Order Systems 7109.11 The Stability Problem 7139.12 Routh–Hurwitz Criterion 7179.13 Root Locus Method 7219.14 Nyquist Stability Criterion 7309.15 Bode Diagram 7369.16 Sampled-Data Systems 7419.17 Exploring Concepts with MATLAB 7519.18 Summary 755Further Reading 756Additional Problems 757Advanced Problems 760Computer Experiments 765Chapter 10 Epilogue 76910.1 Introduction 76910.2 Speech Signals: An Example of Nonstationarity 77010.3 Time–Frequency Analysis 77110.4 Nonlinear Systems 78210.5 Adaptive Filters 78910.6 Concluding Remarks 792Further Reading 792Appendix A Selected Mathematical Identities 795A. 1 Trigonometry 795A. 2 Complex Numbers 796A. 3 Geometric Series 797A. 4 Definite Integrals 797A. 5 Matrices 798Appendix B Partial-Fraction Expansions 800B. 1 Partial-Fraction Expansions of Continuous-Time Representations 800B. 2 Partial-Fraction Expansions of Discrete-Time Representation 803Appendix C Tables of Fourier Representations and Properties 806C. 1 Basic Discrete-Time Fourier Series Pairs 806C. 2 Basic Fourier Series Pairs 807C. 3 Basic Discrete-Time Fourier Transform Pairs 807C. 4 Basic Fourier Transform Pairs 808C. 5 Fourier Transform Pairs for Periodic Signals 808C. 6 Discrete-Time Fourier Transform Pairs for Periodic Signals 809C. 7 Properties of Fourier Representations 810C. 8 Relating the Four Fourier Representations 812C. 9 Sampling and Aliasing Relationships 812Appendix D Tables of Laplace Transforms and Properties 814D. 1 Basic Laplace Transforms 814D. 2 Laplace Transform Properties 815Appendix E Tables of z-Transforms and Properties 817E.1 Basic z-Transforms 817E.2 z-Transform Properties 818Appendix F Introduction to MATLAB 819F. 1 Basic Arithmetic Rules 819F. 2 Variables and Variable Names 820F. 3 Vectors and Matrices 820F. 4 Plotting in MATLAB 823F. 5 M-files 824F. 6 Additional Help 825Index 827

Simon Haykin, PhD, is University Professor and Director of the Adaptive Systems Laboratory at McMaster University.Barry Van Veen, University of Wisconsin.

• Preface viiNotation xviiChapter 1 Introduction 11.1 What Is a Signal? 11.2 Classification of Signals 21.3 Basic Operations on Signals 111.4 Elementary Signals 191.5 What Is a System? 381.6 Overview of Specific Systems 391.7 Systems Viewed as Interconnections of Operations 521.8 Properties of Systems 541.9 Noise 681.10 Theme Examples 711.11 Exploring Concepts with MATLAB 801.12 Summary 86Further Reading 87Additional Problems 88Advanced Problems 94Computer Experiments 97Chapter 2 Time-Domain Representations of Linear Time-Invariant Systems 992.1 Introduction 992.2 The Convolution Sum 1002.3 Convolution Sum Evaluation Procedure 1042.4 The Convolution Integral 1182.5 Convolution Integral Evaluation Procedure 1202.6 Interconnections of LTI Systems 1322.7 Relations Between LTI System Properties and the Impulse Response 1382.8 Step Response 1442.9 Differential and Difference Equation Representations of LTI Systems 1462.10 Solving Differential and Difference Equations 1532.11 Characteristics of Systems Described by Differential and Difference Equations 1632.12 Block Diagram Representations 1692.13 State-Variable Descriptions of LTI Systems 1742.14 Exploring Concepts with MATLAB 1842.15 Summary 190Further Reading 191Additional Problems 192Advanced Problems 201Computer Experiments 203Chapter 3 Fourier Representations of Signals and Linear Time-Invariant Systems 2053.1 Introduction 2053.2 Complex Sinusoids and Frequency Response of LTI Systems 2063.3 Fourier Representations for Four Classes of Signals 2093.4 Discrete-Time Periodic Signals: The Discrete-Time Fourier Series 2123.5 Continuous-Time Periodic Signals: The Fourier Series 2253.6 Discrete-Time Nonperiodic Signals: The Discrete-Time Fourier Transform 2413.7 Continuous-Time Nonperiodic Signals: The Fourier Transform 2523.8 Properties of Fourier Representations 2653.9 Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions 3113.10 Parseval Relationships 3173.11 Time−Bandwidth Product 3193.12 Duality 3213.13 Exploring Concepts with MATLAB 3273.14 Summary 335Further Reading 336Additional Problems 337Advanced Problems 348Computer Experiments 353Chapter 4 Applications of Fourier Representations to Mixed Signal Classes 3574.1 Introduction 3574.2 Fourier Transform Representations of Periodic Signals 3584.3 Convolution and Multiplication with Mixtures of Periodic and Nonperiodic Signals 3644.4 Fourier Transform Representation of Discrete-Time Signals 3754.5 Sampling 3794.6 Reconstruction of Continuous-Time Signals from Samples 3884.7 Discrete-Time Processing of Continuous-Time Signals 4004.8 Fourier Series Representations of Finite-Duration Nonperiodic Signals 4074.9 The Discrete-Time Fourier Series Approximation to the Fourier Transform 4144.10 Efficient Algorithms for Evaluating the DTFS 4224.11 Exploring Concepts with MATLAB 4264.12 Summary 429Further Reading 430Additional Problems 431Advanced Problems 436Computer Experiments 440Chapter 5 The Laplace Transform 4435.1 Introduction 4435.2 The Laplace Transform 4435.3 The Unilateral Laplace Transform 4515.4 Properties of the Unilateral Laplace Transform 4525.5 Inversion of the Unilateral Laplace Transform 4575.6 Solving Differential Equations with Initial Conditions 4625.7 Laplace Transform Methods in Circuit Analysis 4675.8 Properties of the Bilateral Laplace Transform 4705.9 Properties of the Region of Convergence 4735.10 Inversion of the Bilateral Laplace Transform 4775.11 The Transfer Function 4815.12 Causality and Stability 4845.13 Determining the Frequency Response from Poles and Zeros 4895.14 Exploring Concepts with MATLAB 5025.15 Summary 505Further Reading 507Additional Problems 507Advanced Problems 511Computer Experiments 513Chapter 6 The z-Transform 5156.1 Introduction 5156.2 The z-Transform 5156.3 Properties of the Region of Convergence 5246.4 Properties of the z-Transform 5296.5 Inversion of the z-Transform 5356.6 The Transfer Function 5436.7 Causality and Stability 5476.8 Determining the Frequency Response from Poles and Zeros 5536.9 Computational Structures for Implementing Discrete-Time LTI Systems 5596.10 The Unilateral z-Transform 5626.11 Exploring Concepts with MATLAB 5686.12 Summary 571Further Reading 572Additional Problems 572Advanced Problems 576Computer Experiments 579Chapter 7 Application to Communication Systems 5817.1 Introduction 5817.2 Types of Modulation 5817.3 Benefits of Modulation 5857.4 Full Amplitude Modulation 5877.5 Double Sideband-Suppressed Carrier Modulation 5967.6 Quadrature-Carrier Multiplexing 6017.7 Other Variants of Amplitude Modulation 6027.8 Pulse-Amplitude Modulation 6077.9 Multiplexing 6117.10 Phase and Group Delays 6167.11 Exploring Concepts with MATLAB 6207.12 Summary 630Further Reading 631Additional Problems 632Advanced Problems 635Computer Experiments 637Chapter 8 Application to Filters and Equalizers 6398.1 Introduction 6398.2 Conditions for Distortionless Transmission 6398.3 Ideal Low-Pass Filters 6428.4 Design of Filters 6488.5 Approximating Functions 6498.6 Frequency Transformations 6568.7 Passive Filters 6588.8 Digital Filters 6598.9 FIR Digital Filters 6618.10 IIR Digital Filters 6708.11 Linear Distortion 6758.12 Equalization 6768.13 Exploring Concepts with MATLAB 6808.14 Summary 685Further Reading 685Additional Problems 686Advanced Problems 688Computer Experiments 689Chapter 9 Application to Linear Feedback Systems 6919.1 Introduction 6919.2 What Is Feedback? 6919.3 Basic Feedback Concepts 6939.4 Sensitivity Analysis 6969.5 Effect of Feedback on Disturbance or Noise 6989.6 Distortion Analysis 6999.7 Summarizing Remarks on Feedback 7019.8 Operational Amplifiers 7019.9 Control Systems 7079.10 Transient Response of Low-Order Systems 7109.11 The Stability Problem 7139.12 Routh–Hurwitz Criterion 7179.13 Root Locus Method 7219.14 Nyquist Stability Criterion 7309.15 Bode Diagram 7369.16 Sampled-Data Systems 7419.17 Exploring Concepts with MATLAB 7519.18 Summary 755Further Reading 756Additional Problems 757Advanced Problems 760Computer Experiments 765Chapter 10 Epilogue 76910.1 Introduction 76910.2 Speech Signals: An Example of Nonstationarity 77010.3 Time–Frequency Analysis 77110.4 Nonlinear Systems 78210.5 Adaptive Filters 78910.6 Concluding Remarks 792Further Reading 792Appendix A Selected Mathematical Identities 795A. 1 Trigonometry 795A. 2 Complex Numbers 796A. 3 Geometric Series 797A. 4 Definite Integrals 797A. 5 Matrices 798Appendix B Partial-Fraction Expansions 800B. 1 Partial-Fraction Expansions of Continuous-Time Representations 800B. 2 Partial-Fraction Expansions of Discrete-Time Representation 803Appendix C Tables of Fourier Representations and Properties 806C. 1 Basic Discrete-Time Fourier Series Pairs 806C. 2 Basic Fourier Series Pairs 807C. 3 Basic Discrete-Time Fourier Transform Pairs 807C. 4 Basic Fourier Transform Pairs 808C. 5 Fourier Transform Pairs for Periodic Signals 808C. 6 Discrete-Time Fourier Transform Pairs for Periodic Signals 809C. 7 Properties of Fourier Representations 810C. 8 Relating the Four Fourier Representations 812C. 9 Sampling and Aliasing Relationships 812Appendix D Tables of Laplace Transforms and Properties 814D. 1 Basic Laplace Transforms 814D. 2 Laplace Transform Properties 815Appendix E Tables of z-Transforms and Properties 817E.1 Basic z-Transforms 817E.2 z-Transform Properties 818Appendix F Introduction to MATLAB 819F. 1 Basic Arithmetic Rules 819F. 2 Variables and Variable Names 820F. 3 Vectors and Matrices 820F. 4 Plotting in MATLAB 823F. 5 M-files 824F. 6 Additional Help 825Index 827