In Continuous Time (eBook)

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Weigang Zhang, Chang’an University, Xi’an, China

Table of content:
Chapter 1 Signals
1.1 Definition of Signals
1.2 Classification of Signals
1.2.1 Periodic and Aperiodic Signals
1.2.2 Energy and Power Signals
1.2.3 Analog and Digital Signals
1.2.4 Certain and Random Signals
1.3 Basic Continuous-Time Signals
1.3.1 Direct Current Signals
1.3.2 Sinusoidal Signals
1.3.3 Exponential Signals
1.3.4 Complex Exponential Signals
1.3.5 Symbol Signal
1.3.6 Unit Ramp Signal
1.3.7 Unit Step Signal
1.3.8 Unit Impulse Signal
1.3.9 Unit Doublets Signal
1.4 Operation of Continuous-Time signals BR />1.4.1 Arithmetic Operation BR />1.4.2 Time Shifting Transform
1.4.3 Reversal Transform
1.4.4 Scaling Transform
1.4.5 Decomposition and Composition
1.4.6 Plotting of Signals
1.5 Learning Tip
1.6 Exercises
Chapter 2 Systems
2.1 Definition of Systems
2.2 State and Response of Systems
2.3 Classification of Systems
2.3.1 Linear and Nonlinear Systems
2.3.2 Time Variant and Invariant Systems
2.3.3 Dynamic and Non-Dynamic Systems BR />2.3.4 Continuous- and Discrete-Systems
2.3.5 Causal and Non-Casual Systems
2.3.6 Open-loop and Closed-loop Systems BR />2.3.7 Stable and Unstable Systems
2.3.8 Lumped-Parameter and Distributed-Parameter Systems
2.4 System Model and Operation Block Diagram BR />2.4.1 System Model
2.4.2 Operation Block Diagram
2.5 Learning Tip
2.6 Exercises
Chapter 3 Time-Domain Analysis for Continuous-Time System ;
3.1 Analytical Method of Differential Equation
3.1.1 Classical Analytical Method
3.1.2 Response Decomposition Method
3.2 Impulse Response and Step Response
3.2.1 Impulse Response
3.2.2 Step Response
3.3 Operator Analysis
3.2.1 Differential Operator and Transfer Operator
3.3.2 Determine Impulse Response by Transfer Operator
3.4 Convolution Method
3.4.1 Definition of Convolution
3.4.2 Properties of Convolution
3.4.3 Determine Zero-State Response by Convolution
3.5 Learning Tip
3.6 Exercises
Chapter 4 Real Frequency-Domain Analysis for Periodic Signals of Continuous-Time System
4.1 Orthogonal Functions
4.1.1 Orthogonal Function Set
4.1.2 Triangle Function Set
4.1.3 Imaginary Exponent Function Set
4.2 Fourier Series
4.2.1 Triangular Form of Fourier Series
4.2.2 Function Symmetry and Fourier Coefficient
4.2.3 Exponential Form of Fourier Series
4.2.4 Properties of Fourier Series
4.3 Frequency Spectrum of Signals
4.3.1 Definition of Frequency Spectrum
4.3.2 Characteristics of Frequency Spectrum
4.4 Fourier Series Analysis Method for Systems
4.4.1 System Function
4.4.2 Fourier Series Analysis Method
4.5 Learning Tip
4.6 Exercises
Chapter 5 Real Frequency-Domain Analysis for Aperiodic Signals of Continuous-Time System
5.1 Fourier Transform
5.1.1 Definition of Fourier Transform
5.1.2 Fourier Transform of Typical Aperiodic Signals
5.2 Properties of Fourier Transform
5.2.1 Linearity
5.2.2 Time Shifting
5.2.3 Frequency Shifting
5.2.4 Scaling Transform
5.2.5 Symmetry
5.2.6 Properties of Convolution
5.2.7 Differential in Time-Domain
5.2.8 Integration in Time-Domain
5.2.9 Modulation
5.3 Fourier Transform of Periodic Signals
5.4 Solution for Inverse Fourier Transform
5.5 Fourier Transform Analysis for Aperiodic Signals
5.5.1 System Model Analysis
5.5.2 System Function Analysis
5.5.3 Signal Decomposition Analysis
5.6 Fourier Transform Analysis for Periodic Signals
5.7 Undistorted Transmission Condition
5.8 Hilbert Transform
5.9 Disadvantages of Fourier Transform Analysis
5.10 Learning Tip
5.11 Exercises
Chapter 6 ; Complex Frequency-Domain Analysis for Continuous-Time System
6.1 Laplace Transform
6.1.1 Definition of Laplace Transform
6.1.2 Laplace Transform of Common Signals
6.1.3 Laplace Transform of Periodic Signals
6.2 Properties of Laplace Transform
6.2.1 Linearity
6.2.2 Time Shifting
6.2.3 Complex Frequency Shifting
6.2.4 Scaling Transform
6.2.5 Differential in Time-Domain
6.2.6 Integration in Time-Domain
6.2.7 Convolution Theorem
6.2.8 Initial-Value Theorem
6.2.9 Final-Value Theorem
6.2.10 Differential in Frequency-Domain
6.2.11 Integration in Frequency-Domain
6.3 Solution for Inverse Laplace transform
6.4 System Function Analysis in Complex Frequency-Domain
6.4.1 System Function
6.4.2 Analysis Method of System Function
6.5 Model Analysis in Complex Frequency-Domain
6.5.1 System Model Analysis
6.5.2 Circuit Model in Complex Frequency-Domain
6.6 Analysis of Signal Decomposition in Complex Frequency-Domain
6.7 Learning Tip
6.8 Exercises
Chapter 7 Emulation and Stability Analysis of Continuous-Time System
7.1 System Analysis
7.1.1 Basic Arithmetic Unit
7.1.2 Emulation of System Block Diagram
7.1.3 Emulation of System Flow Diagram
7.2 Stability Analysis of Systems
7.2.1 Stability of Systems
7.2.2 Zeros and Poles Analysis of System Function H(s)
7.2.3 Determination of System Stability
7.3 Learning Tip
7.4 Exercises
Chapter 8 Discrete Signals and Systems Analysis in Time-Domain
8.1 Basic Discrete Signals
8.1.1 Sinusoidal-Train
8.1.2 Complex exponential-Train
8.1.3 Exponential-Train
8.1.4 Unit Step-Train
8.1.5 Unit Impulse-Train
8.1.6 Z-Train
8.2 Sequence fundamental operation
8.2.1 Four arithmetic operations
8.2.2 Time shifting
8.2.3 Reversal
8.2.4 Cumulative-Sum
8.2.5 Differential
8.2.6 Overlapping
8.2.7 Convolution-Sum
8.3 Time-domain description for discrete system
8.3.1 Differential equation description method
8.3.2 Operator description method
8.3.3 Convolution sum description method
8.4 Time-domain analysis for discrete system
8.4.1 Classical analysis method in time-domain
8.4.2 Unit impulse response
8.4.3 Analysis method of response decomposition
8.5 Learning tip
8.6 Exercises
Chapter 9 Discrete signal and system analysis in z-domain
9.1 z-Transform
9.1.1 Definition of z-Transform
9.1.2 z-Transform of Typical Train
9.1.3 Properties of z-transform
9.1.4 Solution of inverse z- transform
9.1.5 Relationship between z- and s-domain
9.2 Discrete system analysis in z-domain
9.2.1 Differential equation analysis method
9.2.2 System function analysis method
9.2.3 Sequence decomposition analysis method
9.3 Emulation of discrete system
9.4 Stability analysis of discrete system
9.5 Frequency properties of discrete system
9.6 Learning tip
9.7 Exercises
Chapter 10 State-space analysis of system
10.1 State-space description of system
10.2 State equation of system
10.3 Establishment of state equation
10.3.1 Circuit diagram establishment method
10.3.2 Analog diagram establishment method
10.3.3 Mathematical model (or system function) establishment method
10.4 Solution of state equation
10.4.1 Solution in frequency-domain
10.4.2 Solution in time-domain
10.4.3 Calculation of eAt
10.5 Stability identification
10.6 Learning tip
10.7 Exercises
Chapter 11： System synthesis summarize
11.1 Definition of network and two-port network
11.2 Equation and parameters of two-port network
11.2.1 Z equation and parameters
11.2.2 Y equation and parameters
11.3 Condition to achieve passive system synthesis
11.4 Passive One-port Network Synthesis for Continuous-Time System
11.4.1 R-C synthesis
11.4.2 R-L synthesis
11.4.3 L-C synthesis
11.5 Learning tip
11.6 Exercises
Appendix A Solutions to The Exercises
Appendix B Tables of Transformations
Bibliography