1 SIGNALS AND SYSTEMS 1.0 Introduction 1.1 Continuous-Time and Discrete-Time Signals 1.1.1 Examples and Mathematical Representation 1.1.2 Signal Energy and Power 1.2 Transformations of the Independent Variable 1.2.1 Examples of Transformations of the Independent Variable 1.2.2 Periodic Signals 1.2.3 Even and Odd Signals 1.3 Exponential and Sinusoidal Signals 1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals 1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals 1.3.3 Periodicity Properties of Discrete-Time Complex Exponentials 1.4 The Unit Impulse and Unit Step Functions 1.4.1 The Discrete-Time Unit Impulse and Unit Step Sequences 1.4.2 The Continuous-Time Unit Step and Unit Impulse Functions 1.5 Continuous-Time and Discrete-Time System l.5.1 Simple Examples of Systems 1.5.2 Interconnections of Systems 1.6 Basic System Properties 1.6.1 Systems with and without Memory 1.6.2 Invertibility and Inverse Systems 1.6.3 Causality 1.6.4 Stability 1.6.5 Time Invariance 1.6.6 Linearity 1.7 Summary Problems LINEAR TIME-INVARIANT SYSTEMS 2.0 Introduction 2.1 Discrete-Time LTI Systems: The Convolution Sum 2.1.1 The Representation of Discrete-Time Signals in Terms of Impulses 2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems 2.2 Continunus-Time LTI Systems: The Convolution Integral 2.2.1 The Representation of Continuous-Time Signals in Terms of Impulses 2.2.2 The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems 2.3 Properties of Linear Time-Invariant Systems 2.3.1 The Commutative Property 2.3.2 The Distributive Property 2.3.3 The Associative Property ' 2.3.4 LTI Systems with and without Memory 2.3.5 Invenibility of LTI Systems 2.3.6 Cansality for LII Systems 2.3.7 Stability for LTI Systems 2.3.8 The Unit Step Response of an LTI System 2.4 Causal LTI Systems Described by Differential and Difference Equations 2.4.1 Linear Constant-Coefficient Differential Equations 2.4.2 Linear Constant-CoeHicient Difference Equations 2.4.3 Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations 2.5 Singularity Functions 2.5.1 The Unit Impulse as an Idealized Short Pulse 2.5.2 Defining the Unit Impulse through Convolution 2.5.3 Unit Doublets and Other Singulanty Functions 2.6 Summary Problems 3 FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS 3.0 Introduction 3.1 A Historieal Perspective 3.2 The Response of LTI Systems to Complex Exponentials 3.3 Fourier Series Representation of Continuous-Time Periodic Signals 3.3.1 Linear Combinations of Harmonically Related Complex Exponentials 3.3.2 Determination of the Fourier Series Representation of a Continuous-Time Periodic Signal 3.4 Convergence of the Fourier Series 3.5 Properties of Continuous-Time Fourier Series 3.5.1 Linearity 3.5.2 Time Shifting 3.5.3 Time Reversal 3.5.4 Time Scaling 3.5.5 Multiplication 3.5.6 Conjugation and Conjugate Symmetry 3.5.7 Parseval's Relation for Continuous-Time Periodic Signals 3.5.8 Summary of Propenies of the Continuous-Time Fourier Series 3.5.9 Examples 3.6 Fourier Series Representation of Discrete-Time Periodic Signals 3.6.1 Linear Combinations of Harmonically Related Complex Exponentials 3.6.2 Determination of the Fourier Series Representation of a Periodic Signal 3.7 Propedies of Discrete-Time Fourier Series 3.7.1 Multiplication 3.7.2 First Difference 3.7.3 Parseval's Relation for Discrete-Time Periodic Signals 3.7.4 Examples 3.8 Fourier Series and LTI Systems 3.9 Filtering 3.9.1 Frequency-Shaping Filters 3.9.2 Frequency-Selective Filters 3.10 Examples of Continuous-Time Filters Described by Differential Equations 3.10.1 A Simple RC Lowpass Filter 3.10.2 A Simple RC Highpass Filter 3.11 Examples of Discrete-Time Filters Described by Difference Equations 3.11.1 First-Order Recursive Discrete-Time Filters 3.11.2 Nonrecursive Discrete-Time Filters 3.12 Summary Problems 4 THE CONTINUOUS-TIME FOURIER TRANSFORM 4.0 Introduction 4.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform 4.1.1 Development of the Fourier Transform Representation of an Aperiodic Signal 4.1.2 Convergence of Fourier Transforms 4.1.3 Examples of Continuous-Time Fourier Transforms 4.2 The Fourier Tkansform for Periodic Signals 4.3 Properties of the Continuous-Time Fourier Transform 4.3.1 Linearity 4.3.2 Time Shifting 4.3.3 Conjugation and Conjugate Symmetry 4.3.4 Differentiation and Integration 4.3.5 Time and Frequency Scaling 4.3.6 Duality 4.3.7 Parseval's Relation 4.4 The Convolution Property 4.4.1 Examples 4.5 Ihe Multiplication Property 4.5.1 Frequency-Selective Filtering with Variable Center Frequency 4.6 Tables of Fourier Properties and of Basic Fourier Transform Pairs 4.7 Systems Characterized by Linear Constant-Coefficient Differential Equations 4.8 Summary Problems 5 THE DISCRETE-TIME FOURIER TRANSFORM 5.0 Introduction 5.1 Representation of Aperiodic Signals: The Discrete-Time Fourier Transform 5.1.1 Development of the Discrete-Time Fourier Transform 5.1.2 Examples of Discrete-Time Fourier Transforms 5.1.3 Convergence Issues Associated with the Discrete-Time Fourier Transform 5.2 The Fourier Transform for Periodic Signals 5.3 Properties of the Discrete-Time Fourier Transform 5.3.1 Periodicity of the Discrete-Time Fourier Transform 5.3.2 Linearity of the Fourier Transform 5.3.3 Time Shifting and Frequency Shifting 5.3.4 Conjugation and Conjugate Symmetry 5.3.5 Differencing and Accumulation 5.3.6 Time Reversal 5.3.7 Time Expansion 5.3.8 Differentiation in Frequency 5.3.9 Parseval's Relation 5.4 The Convolution Property 5.4.1 Examples 5.5 The Multiplication Property 5.6 Tables of Fourier Iransform Properties and Basic Fourier Transform Pairs 5.7 Duality 5.7.1 Duality in the Discrete-Time Fourier Series 5.7.2 Duality between the Discrete-Time Fourier Transform and the Continuous-Time Fourier Series S.8 Systems Characterized by Linear Constant-Coefficient Difference Equations 5.9 Summary Problems 6 TIME AND FREQUENCY C OF SIGNALS AND SYSTEMS 6.0 Introduction 6.1 The Magnitude-phase Representation of the Fourier Transform 6.2 The Magnitude-Phase Representation of the Frequency R of LTI Systems 6.2.1 Linear and Nonlinear Phase 6.2.2 Group Delay 6.2.3 Log-Magnitude and Bode Plots 6. 3 Time-Domain Properties of Ideal Frequency-Selective Filters 6.4 Time-Domain and Frequency-Domain Aspects of Nonideal Filters 6. 5 First-Order and Second-Order Continuous-Time Systems 6.5.1 First-Order Continuous-Time Systems 6.5.2 Second-Order Continuous-Time Systems 6.5.3 Bode Plots for Rational Frequency Responses 6.6 First-Order and Second-Order Discrete-Time Systems 6.6.1 First-Order Discrete-Time Systems 6.6.2 Second-Order Discrete-Time Systems 6.1 Examples of Time-and Frequency-Domain Analysis of Systems 6.7.1 Analysis of an Automobile Suspension System 6.7.2 Examples of Discrete-Time Nonrecursive Filters 6.8 Summary Problems 7 SAMPLING 7.0 Introduction 7.1 Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem 7. 1.1 Impulse-Train Sampling 7. 1.2 Sampling with a 7.2 Reconstruction of a Signal from Its Samplee Using Interpolation 7.3 The Effect of Undersampling: Aliasing 7.4 Discrete-Time 7.4.1 Digital Differentiator 7.4.2 Half-Sample Delay 7. 5 Sampling of Discrete-Time Signals 7.5.1 Impulse-Train Sampling 7.5.2 Discrete-Time Decimation and Interpolation 7.6 S Problems 8 Co 8.0 Introduction 8.1 Complex 8.1.1 Amplitude Modulation with a Complex Exponential Carrier 8.1.2 Amplitude Modulation with a Sinusoidal Carrier 8.2 Demodulatiou for Sinusoidal AM 8.2.1 Synchronous Demodulation 8.2.2 Asynchronous Demodulation 8.3 Frequency-Division Multiplexing 8.4 Single-Sideband Sinusoidal Amplitude Modulation 8.5 Amplitude Modulation with a Pulse-Train Carrier 8.5.1 Modulation of a Pulse-Train Carrier 8.5.2 Time-Division Multiplexing 8.6 Pulse-Amplitude Modulation 8.6.1 Pulse-Amplitude Modulated Signals 8.6.2 Intersymbol Interference in PAM Systems 8.6.3 Digital Pulse-Amplitude and Pulse-Code Modulation 8.7 Sinusoidal Frequency Modulation 8.7.1 Narrowband Frequency Modulation 8.7.2 Wideband Frequency Modulation 8.7.3 Periodic Square-Wave Modulating Signal 8.8 Discrete-Time Medulation 8.8.1 Discrete-Time Sinusoidal Amplitude Modulation 8.8.2 Discrete-Time Transmodulation 8.9 S Problems 9 THE LAPLACE TRANSFORM 9.0 Introduction 9.1 The Laplace Transform 9.2 The Region of Convergence for Laplace Transforms 9.3 The Inverse Laplace Transform 9.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot 9.4.1 First-Order Systems 9.4.2 Second-Order Systems 9.4.3 All-Pass Systems 9.5 Properties of the Laplace Transform 9.5.1 Linearity of the Laplace Transform 9.5.2 Time Shifting 9.5.3 Shifting in the s-Domain 9.5.4 Time Scaling 9.5.5 Conjugation 9.5.6 Convolution Property 9.5.7 Differentiation in the Time Domain 9.5.8 Differentiation in the s-Domain 9.5.9 Integration in the Time Domain 9.5.1O The Initial- and Final-Value Theorems 9.5.11 Table of Properties 9.6 Some Laplace Transform Pairs 9.7 Analysis and Characterization of LTI Systems Dsing the Laplace Transform 9.7.1 Causality 9.7.2 Stability 9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations 9.7.4 Examples Relating System Behavior to the System Function 9.7.5 Butterworth Filters 9.8 System Function Algebra and Block Representations 9.8.1 System Functions for Interconnections of LTI Systems 9.8.2 Block Diagram Representations for Causal LTI Systems Described by Differential Equations and Rational System Functions 9.9 The Unilateral Laplace Transform 9.9.1 Examples of Unilateral Laplace Transforms 9.9.2 Properties of the Unilateral Laplace Transform 9.9.3 Solving Differential Equations Using the Unilateral Laplace Transform 9.10 S Problems 10 THE Z-TRANSFORM 10.0 Introduction 10.1 The z-Transform 10.2 The Region of Convergence for the z-Transform 10.3 The Inverse z-Transform 10.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot 10.1.1 First-Order Systems 10.4.2 Second-Order Systems 10.5 Properties of the z-Transform 10.5.1 Linearity 10.5.2 Time Shifting 10.5.3 Scaling in the z-Domain 10.5.4 Time Reversal 10.5.5 Time Expansion 10.5.6 Conjugation 10.5.7 The Convolution Property 10.5.8 Differentiation in the z-Domain 10.5.9 Ihe Initial-Value Theorem 10.5.10 S 10.6 Some Common z-Transform Pairs 10.1 Analysis and Characterization of LTI Systems Using z-Transforms 10.7.1 Causality 10.7.2 Stability 10.7.3 LTI Systems Characterized by Linear Constant-Coefficient Difference Equations 10.7.4 Examples Relating System Behavior to the System Function 10.8 System Function Algebra and Block Diagram Representations 10.8.1 System Functions for Interconnections of LTI Systems 10.8.2 Block Diagram Representations for Causal LTI Systems Described by Difference Equations and Rational System Functions 10.9 The Unilateral z-Transform 10.9.1 Examples of Unilateral z-Transforms and Inverse Transforms 10.9.2 Properties of the Unilateral z-Transform 10.9.3 Solving Difference Equations Using the Unilateral z-Transform 10.10 S Problems 11 LINEAR FEEDBACK SYSTEMS 11.0 Introduction 11.1 Linear Feedback Systems 11.2 Some Applications and Consequences of Feedback 11.2.1 Inverse System Design 11.2.2 Compensation for Nonideal Elements 11.2.3 Stabilization of Unstable Systems 11.2.4 Sampled-Data Feedback Systems 11.2.5 Tracking System 11.2.6 Destabilization Caused by Feedback 11.3 Root-Loeus Analysls of Linear Feedbaek Systems 11.3.1 An Introductory Example 11.3.2 Equation for the Closed-Loop Poles 11.3.3 The End Points of the Root Locus: The Closed-Loop Poles for K=O and |K|= + 11.3.4 The Angle Criterion 11.3.5 Properties of the Root Locus 11.4 The Nyquist Stability Criterion 11.4.1 The Encirclement Property 11.4.2 The Nyquist Criterion for Continuous-Time LTI Feedback Systems 11.4.3 The Nyquist Criterion for Discrete-Time LTI Feedback Systems 11.5 Gain and Phase 11.6 S Problems APPENDIX PARTIAL-FRACTION EXPANSION BIBLIOGRAPHY ANSWERS INDEX
鄂公網(wǎng)安備 42010302001612號 