Weakly Nonlinear Systems : : With Applications in Communications Systems.
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| Superior document: | Understanding Complex Systems Series |
|---|---|
| : | |
| Place / Publishing House: | Cham : : Springer International Publishing AG,, 2023. Ã2024. |
| Year of Publication: | 2023 |
| Edition: | 1st ed. |
| Language: | English |
| Series: | Understanding Complex Systems Series
|
| Online Access: | |
| Physical Description: | 1 online resource (376 pages) |
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Table of Contents:
- Intro
- Foreword
- Preface
- Contents
- 1 Introduction
- 1.1 Nonlinear Phenomena
- 1.1.1 Multiple Equilibrium Points
- 1.1.2 Limit Cycles
- 1.1.3 Bifurcations
- 1.1.4 Chaos
- 1.2 Weakly-Nonlinear Systems
- 1.3 Distributions
- 1.4 Numerical Simulations
- 1.5 Historical Notes
- Part I Signals
- 2 Distributions
- 2.1 Test Functions
- 2.2 Distributions
- 2.3 Basic Properties
- 2.4 Differentiation of Distributions
- 2.5 Distributions with Compact Support
- 2.5.1 Single-Point Support
- 3 Convolution of Distributions
- 3.1 Tensor Product
- 3.2 Convolution of Distributions
- 3.3 Approximation of Distributions
- 3.4 Convolution of Periodic Distributions
- 4 Fourier Transform of Distributions
- 4.1 Test Functions of Fast Descent
- 4.2 Fourier Transform of Tempered Distributions
- 4.3 Distributions with Bounded Support
- 4.4 Fourier Transform and Convolution
- 4.5 Periodic Distributions
- 4.6 Extension to Several Variables
- 5 Laplace Transform of Distributions
- 5.1 Definition
- 5.2 Properties
- 5.3 Inverse Laplace Transform
- 5.4 Extension to Several Variables
- 6 Summable Distributions
- 6.1 Definition and Canonical Extension
- 6.2 Convolution of Summable Distributions
- 6.3 Fourier Transform of Summable Distributions
- Part II Systems
- 7 Convolution Equations
- 7.1 Convolution Algebra
- 7.2 Convolution Equations
- 7.3 Initial Value Problems
- 7.4 Integro-Differential Equations
- 7.5 Periodic Solutions
- 7.6 General Convolution Equations
- 7.6.1 General Solutions
- 7.6.2 Tempered Solutions
- 7.7 Systems of Convolution Equations
- 8 Linear Time Invariant Systems
- 8.1 Basic Definitions
- 8.2 Causality
- 8.3 Stability
- 8.4 Transfer Function
- 8.4.1 Stable Systems
- 8.4.2 Causal Systems
- 8.5 Rational Transfer Functions
- 8.6 System State
- 8.6.1 Controllability
- 8.6.2 Observability.
- 8.6.3 Jordan Normal form
- 9 Weakly Nonlinear Time Invariant Systems
- 9.1 Introduction
- 9.2 Graded Algebra of Test Functions
- 9.3 Direct Product of Distributions
- 9.4 Symmetric Distributions
- 9.5 Weakly Nonlinear Systems
- 9.6 Nonlinear Transfer Functions
- 9.7 Periodic Input Signals
- 9.8 Multi-tone Input Signals
- 9.8.1 General Case
- 9.8.2 Real Case
- 10 Composition of Weakly Nonlinear Time Invariant Systems
- 10.1 Cascade of Noninteracting Systems
- 10.2 Feedback
- 10.3 Linearisation
- 10.4 System Manipulations
- 10.5 Structure
- 11 Weakly Nonlinear Time Invariant Circuits
- 11.1 Metrics for Nonlinear Effects
- 11.1.1 Gain Compression and Expansion
- 11.1.2 Intermodulation
- 11.1.3 Desensitisation
- 11.2 Nonlinear Two-Terminal Elements
- 11.2.1 Nonlinear Resistors
- 11.2.2 Nonlinear Capacitors
- 11.2.3 Nonlinear Inductors
- 11.3 Nonlinear Multi-port Elements
- 11.4 Low-Pass Filter with Nonlinear Capacitor
- 11.4.1 Nonlinear Transfer Functions
- 11.4.2 Second Order Intermodulation
- 11.4.3 Third Order Intermodulation
- 11.4.4 Large Signal Effects
- 11.5 Class-AC Common-Source Stage
- 11.6 Common-Gate Stage
- 11.6.1 Nonlinear Transfer Functions
- 11.6.2 Cascode
- 11.7 Degenerated Common-Source Stage
- 11.7.1 Nonlinear Transfer Functions
- 11.7.2 Resistive Degeneration
- 11.7.3 Inductive Degeneration
- 11.8 Pseudo-Differential Circuits
- 12 Linear Time-Varying Systems
- 12.1 Linear Time-Varying Systems
- 12.2 Linear Ordinary Differential Equations
- 12.2.1 Fundamental Solution
- 12.2.2 Formal Solution
- 12.2.3 Perturbation Theory
- 12.2.4 Non-smooth Coefficients
- 12.3 Impulse Response Generalisation
- 12.4 Time-Varying Frequency Response
- 12.4.1 Definition
- 12.4.2 Differential Equation
- 12.5 Linear Periodically Time-Varying Systems
- 12.5.1 Floquet Theory.
- 12.5.2 Time-Varying Frequency Response
- 13 Weakly Nonlinear Time-Varying Systems
- 13.1 Weakly Nonlinear Time-Varying Systems
- 13.1.1 Definition
- 13.1.2 Time-Varying Nonlinear Impulse Responses
- 13.1.3 Time-Varying Nonlinear Frequency Responses
- 13.2 Weakly Nonlinear Periodically Time-Varying Systems
- 13.2.1 Discrete Convolution
- 13.2.2 Product of Fourier Series
- 13.2.3 Response to Multi-tones
- 14 Periodically Switched Circuits
- 14.1 Switched Circuits
- 14.2 Voltage-Mode Quadrature Modulator
- 14.2.1 Single Input Response
- 14.2.2 Input Current and Switched Resistor
- 14.2.3 Full Response
- 14.2.4 Carrier Leakage
- 14.2.5 Image-Rejection
- 14.2.6 Effect of Mismatch
- 14.2.7 Second-Order Distortion
- 14.2.8 Third-Order Distortion
- 14.3 Sampling Mixer
- 14.3.1 Time-Varying Impulse Response
- 14.3.2 Time-Varying Transfer Function
- 14.3.3 Selectivity
- 14.3.4 Even Harmonic Response Suppression
- 14.4 N-Path Filters
- 14.4.1 Time-Varying Frequency Response
- 14.4.2 Selectivity
- Appendix A Signal-Flow Graphs
- A.1 Linear Signal-Flow Graphs
- A.1.1 Construction Rules
- A.1.2 Reduction Rules
- A.1.3 Mason's Rule
- A.2 Nonlinear Systems
- A.3 Weakly-Nonlinear Systems
- Appendix References
- Index.