سیستم‌ها و سیگنال‌های خطی: مقدمه‌ای بر

This new resource covers a wide range of content by focusing on theorems and examples to explain key concepts of signals and linear systems theory in fewer than 300 pages. Readers will learn how to compute the impulse response of an electronic circuit, design a filter in the presence of colored noise, and use the Z transform to design a digital filter. The book covers transform theory and statespace analysis and design. Stochastic systems and signals, a topic that has become important recently with the advent of renewable energy, is also presented. The Ergodic theorem is discussed in detail, with specific, real world examples of its application to renewable power and energy systems as well as signal processing systems. The book also provides a self-contained introduction to the theory of probability. Written for the practicing engineer and the student new to the subject, this comprehensive guide includes links to literature and online resources for the reader who wants additional information. In addition to numerous worked examples, this primer includes MATLAB® source code to assist readers with their projects in the field. Linear Systems and Signals: A Primer Contents Preface Part I Time Domain Analysis Chapter 1 Introduction to Signals and Systems 1.1 Signals and Their Classification 1.2 Discrete Time Signals 1.2.1 Discrete Time Simulation of Analog Systems 1.3 Periodic Signals 1.4 Power and Energy in Signals 1.4.1 Energy and Power Signal Examples References Chapter 2 Special Functions and a System Point of View 2.1 The Unit Step or Heaviside Function 2.2 Dirac’s Delta Function d(t) 2.3 The Complex Exponential Function 2.4 Kronecker Delta Function 2.5 A System Point of View 2.5.1 Systems With Memory and Causality 2.5.2 Linear Systems 2.5.3 Time Invariant Systems 2.5.4 Stable Systems 2.6 Summary References Chapter 3 The Continuous Time Convolution Theorem 3.1 Introduction 3.2 The System Step Response 3.2.1 A System at Rest 3.2.2 Step Response s(t) 3.3 The System Impulse Response h(t) 3.4 Continuous Time Convolution Theorem 3.5 Summary References Chapter 4 Examples and Applications of the Convolution Theorem 4.1 A First Example 4.2 A Second Example: Convolving with an Impulse Train 4.3 A Third Example: Cascaded Systems 4.4 Systems and Linear Di ̨erential Equations 4.4.1 Example: A Second Order System 4.5 Continuous Time LTI System Not at Rest 4.6 Matched Filter Theorem 4.6.1 Monte Carlo Computer Simulation 4.7 Summary References Chapter 5 Discrete Time Convolution Theorem 5.1 Discrete Time IR 5.2 Discrete Time Convolution Theorem 5.3 Example: Discrete Convolution 5.4 Discrete Convolution Using a Matrix 5.5 Discrete Time Di ̨erence Equations 5.5.1 Example: A Discrete Time Model of the RL Circuit 5.5.2 Example: The Step Response of a RL Circuit 5.5.3 Example: The Impulse Response of the RL Circuit 5.5.4 Example: Application of the Convolution Theorem to Compute the Step Response 5.6 Generalizing the Results: Discrete TimeSystem of Order N 5.6.1 Constant-Coe ̋cient Di ̨erence Equation of Order N 5.6.2 Recursive Formulation of the Response y[n] 5.6.3 Computing the Impulse Response h[n] 5.7 Summary References Chapter 6 Examples: Discrete Time Systems 6.1 Example: Second Order System 6.2 Numerical Analysis of a Discrete System 6.3 Summary References Chapter 7 Discrete LTI Systems: State Space Analysis 7.1 Eigenanalysis of a Discrete System 7.2 State Space Representation and Analysis 7.3 Solution of the State Space Equations 7.3.1 Computing An 7.4 Example: State Space Analysis 7.4.1 Computing the Impulse Response h[n] 7.5 Analyzing a Damped Pendulum 7.5.1 Solution 7.5.2 Solving the Di ̨erential Equation Numerically 7.5.3 Numerical Solution with Negligible Damping 7.6 Summary References Part II System Analysis Based on Transformation Theory Chapter 8 The Fourier Transform Applied to LTI Systems 8.1 The Integral Transform 8.2 The Fourier Transform 8.3 Properties of the Fourier Transform 8.3.1 Convolution 8.3.2 Time Shifting Theorem 8.3.3 Linearity of the Fourier Transform 8.3.4 Di ̨erentiation in the Time Domain 8.3.5 Integration in the Time Domain 8.3.6 Multiplication in the Time Domain 8.3.7 Convergence of the Fourier Transform 8.3.8 The Frequency Response of a Continuous Time LTI System 8.3.9 Further Theorems Based on the Fourier Transform 8.4 Applications and Insights Based on the Fourier Transform 8.4.1 Interpretation of the Fourier Transform 8.4.2 Fourier Transform of a Pulse (t) 8.4.3 Uncertainty Principle 8.4.4 Transfer Function of a Piece of Conducting Wire 8.5 Example: Fourier Transform of e􀀀 tu(t) 8.5.1 Fourier Transform of u(t) 8.6 The Transfer Function of the RC Circuit 8.7 Fourier Transform of a Sinusoid and aCosinusoid 8.8 Modulation and a Filter 8.8.1 A Design Example 8.8.2 Frequency Translation and Modulation 8.9 Nyquist-Shannon Sampling Theorem 8.9.1 Examples 8.10 Summary References Chapter 9 The Laplace Transform and LTI Systems 9.1 Introduction 9.2 Definition of the Laplace Transform 9.2.1 Convergence of the Laplace Transform 9.3 Examples of the Laplace Transformation 9.3.1 An Exponential Function 9.3.2 The Dirac Impulse 9.3.3 The Step Function 9.3.4 The Damped Cosinusoid 9.3.5 The Damped Sinusoid 9.3.6 Laplace Transform of e-ajt 9.4 Properties of the Laplace Transform 9.4.1 Convolution 9.4.2 Time Shifting Theorem 9.4.3 Linearity of the Laplace Transform 9.4.4 Di ̨erentiation in the Time Domain 9.4.5 Integration in the Time Domain 9.4.6 Final Value Theorem 9.5 The Inverse Laplace Transformation 9.5.1 Proper Rational Function: M < N 9.5.2 Improper Rational Function: M  N 9.5.3 Example: Inverse with a Multiple Pole 9.5.4 Example: Inverse without a Multiple Pole 9.5.5 Example: Inverse with Complex Poles 9.6 Table of Laplace Transforms 9.7 Systems and the Laplace Transform 9.8 Example: System Analysis Based on the Laplace Transform 9.9 Linear Di ̨erential Equations and Laplace 9.9.1 Capacitor 9.9.2 Inductor 9.10 Example: RC Circuit at Rest 9.11 Example: RC Circuit Not at Rest 9.12 Example: Second Order Circuit Not at Rest 9.13 Forced Response and Transient 9.13.1 An Example with a Harmonic Driving Function 9.14 The Transfer Function H(w) 9.15 Transfer Function with Second Order Real Poles 9.16 Transfer Function for a Second Order System with Complex Poles 9.17 Summary References Chapter 10 The z-Transform and Discrete LTI Systems 10.1 The z-Transform 10.1.1 Region of Convergence 10.2 Examples of the z-Transform 10.2.1 The Kronecker Delta d[n] 10.2.2 The Unit Step u[n] 10.2.3 The Sequence anu[n] 10.3 Table of z-Transforms 10.4 Properties of the z-Transform 10.4.1 Convolution 10.4.2 Time Shifting Theorem 10.4.3 Linearity of the z-transform 10.5 The Inverse z-Transform 10.5.1 Example: Repeated Pole 10.5.2 Example: Making use of Shifting Theorem 10.5.3 Example: Using Linearity and the Shifting Theorem 10.6 System Transfer Function for Discrete Time LTI systems 10.7 System Analysis using the z-Transform 10.7.1 Step Response with a Given Impulse Response 10.8 Example: System Not at Rest 10.9 Example: First Order System 10.9.1 Recursive Formulation 10.9.2 Zero Input Response 10.9.3 The Zero State Response 10.9.4 The System Transfer Function H(z) 10.9.5 Impulse Response h[n] 10.10 Second Order System Not at Rest 10.10.1 Numerical Example 10.11 Discrete Time Simulation 10.12 Summary References Chapter 11 Signal Flow Graph Representation 11.1 Block Diagrams 11.2 Block Diagram Simplification 11.3 The Signal Flow Graph 11.4 Mason’s Rule: The Transfer Function 11.5 A First Example: Third Order Low Pass Filter 11.5.1 Making Use of a Graph 11.6 A Second Example: Canonical Feedback System 11.7 A Third Example: Transfer Function of a Block Diagram 11.8 Summary References Chapter 12 Fourier Analysis of Discrete-Time Systems and Signals 12.1 Introduction 12.2 Fourier Transform of a Discrete Signal 12.3 Properties of the Fourier Transform of Discrete Signals 12.4 LTI Systems and Di ̨erence Equations 12.5 Example: Discrete Pulse Sequence 12.6 Example: A Periodic Pulse Train 12.7 The Discrete Fourier Transform 12.8 Inverse Discrete Fourier Transform 12.9 Increasing Frequency Resolution 12.10 Example: Pulse with 1 and N Samples 12.11 Example: Lowpass Filter with the DFT 12.12 The Fast Fourier Transform 12.13 Summary References Part III Stochastic Processes and Linear Systems Chapter 13 Introduction to Random Processes and Ergodicity 13.1 A Random Process 13.1.1 A Discrete Random Process: A Set of Dice 13.1.2 A Continuous Random Process: A Wind Electricity Farm 13.2 Random Variables and Distributions 13.2.1 First Order Distribution 13.2.2 Second Order Distribution 13.3 Statistical Averages 13.3.1 The Ensemble Mean 13.3.2 The Ensemble Correlation 13.3.3 The Ensemble Cross-Correlation 13.4 Properties of Random Processes 13.4.1 Statistical Independence 13.4.2 Uncorrelated 13.4.3 Orthogonal Processes 13.4.4 A Stationary Random Process 13.5 Time Averages and Ergodicity 13.5.1 Implications for a Stationary Random Process 13.5.2 Ergodic Random Processes 13.6 A First Example 13.6.1 Ensemble or Statistical Averages 13.6.2 Time Averages 13.6.3 Ergodic in the Mean and the Autocorrelation 13.7 A Second Example 13.7.1 Ensemble or Statistical Averages 13.7.2 Time Averages 13.8 A Third Example 13.9 Summary References Chapter 14 Spectral Analysis of Random Processes 14.1 Correlation and Power Spectral Density 14.1.1 Properties of the Autocorrelation for a WSS Process 14.1.2 Power Spectral Density of a WSS Random Process 14.1.3 Cross-Power Spectral Density 14.2 White Noise and a Constant Signal (DC) 14.2.1 White Noise 14.2.2 A Constant Signal 14.3 Linear Systems with a Random Process as Input 14.3.1 Cross-Correlation Between Input and Response 14.3.2 Relationship Between PSD of Input and Response 14.4 Practical Applications 14.4.1 Multipath Propagation 14.4.2 White Noise Filtering 14.5 Summary References Chapter 15 Discrete Time Filter Design in the Presence of Noise 15.1 Introduction 15.2 The Prefilter 15.3 Linear Mean-Square Estimation 15.4 Prefilter Design During Pilot Frames 15.5 Evaluating Efvvyg and Efs[n]vg 15.6 Design Example 15.7 Summary References 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