ZT of common signals-Signals and Systems Meng Qiao Southeast University-EEWORLD Training

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Chapter 1：Introduction to Signals and Systems
Chapter 2：The Nature and Status of Signals and Systems Courses
Chapter 3：information transmission system
Chapter 4：Information transfer tasks
Chapter 5：signal concept
Chapter 6：Classification of signals (1)
Chapter 7：Classification of signals (2)
Chapter 8：Simple processing of signals (1)
Chapter 9：Simple processing of signals (2)
Chapter 10：system concept
Chapter 11：Description of the system
Chapter 12：Classification of systems (1)
Chapter 13：Classification of systems (2)
Chapter 14：Incremental linear system; zero input response, zero state response
Chapter 15：Contents of linear non-time-varying system analysis
Chapter 16：Introduction to linear non-time-varying system analysis methods
Chapter 17：ex1.4(1)
Chapter 18：ex1.4(2)
Chapter 19：Time-domain models of continuous-time systems
Chapter 20：Classical solutions to differential equations
Chapter 21：An introduction to modern time domain solutions to differential equations
Chapter 22：Operator representation of differential equations
Chapter 23：Arithmetic rules of differential operators
Chapter 24：Oliver Heaviside
Chapter 25：Formal solution of zero input response of linear time-invariant system
Chapter 26：Initial conditions determine the undetermined coefficients
Chapter 27：Zero input response example explanation
Chapter 28：Introduction to equivalent source solution for zero input response
Chapter 29：Basic ideas for solving zero-state response of linear systems
Chapter 30：Requirements for sub-signals
Chapter 31：step signal
Chapter 32：impulse signal
Chapter 33：The signal is decomposed into the sum of step signals
Chapter 34：The signal is decomposed into the sum of impulse signals
Chapter 35：Duamel Points
Chapter 36：convolution integral
Chapter 37：Convolution definition and calculation
Chapter 38：Properties of convolution
Chapter 39：Convolution of several special signals
Chapter 40：Introduction to system impulse response solution methods
Chapter 41：Solving the impulse response of a first-order system
Chapter 42：Solving the impulse response of a second-order system
Chapter 43：Solving the impulse response of any order system
Chapter 44：Full response time domain method solution process and examples
Chapter 45：Relationship between natural_forced response and zero-input_zero-state response
Chapter 46：The response of some typical signals through the system, as well as a summary of the time domain solution method
Chapter 47：Key and difficult points to analyze and solve for impulse response
Chapter 48：Analysis of key and difficult points in solving convolution integrals
Chapter 49：introduction
Chapter 50：Orthogonal decomposition of vectors
Chapter 51：Orthogonal decomposition of signals
Chapter 52：Analogy of signal and vector decomposition
Chapter 53：The first form of the Fourier series expansion
Chapter 54：The second type of Fourier series expansion
Chapter 55：Direchlet conditions
Chapter 56：The interval of Fourier series expansion
Chapter 57：DC component, fundamental wave and harmonics
Chapter 58：Fourier series expansion of periodic square waves
Chapter 59：Bibbs phenomenon
Chapter 60：Fourier series expansion of the complex sine form
Chapter 61：Odd and even signals and odd and even harmonic signals
Chapter 62：Signal Power and Pasval’s Theorem
Chapter 63：One-sided spectrum
Chapter 64：bilateral spectrum
Chapter 65：Characteristics of periodic signal spectrum
Chapter 66：The impact of changes in time domain parameters on spectrum (1)
Chapter 67：The impact of changes in time domain parameters on spectrum (2)
Chapter 68：Fourier transform
Chapter 69：Inverse Fourier Transform
Chapter 70：Forward and inverse Fourier transform formula
Chapter 71：Spectrum of aperiodic signal
Chapter 72：Various forms of Fourier changes
Chapter 73：Fourier transform of common signals (1)
Chapter 74：Fourier transform of common signals (2)
Chapter 75：Fourier transform of periodic signals
Chapter 76：Linear characteristics, delay characteristics, frequency shift characteristics
Chapter 77：Scale transformation characteristics and odd-even virtual-real characteristics
Chapter 78：Symmetrical and differential properties
Chapter 79：Integral characteristics
Chapter 80：Frequency domain calculus properties
Chapter 81：convolution theorem
Chapter 82：Calculus Properties Application
Chapter 83：Application examples of properties of Fourier transform
Chapter 84：An example of using Fourier transform properties with caution
Chapter 85：power spectrum
Chapter 86：energy spectrum
Chapter 87：Pulse width and frequency band
Chapter 88：Introduction to Fourier
Chapter 89：Overview of time domain analysis method
Chapter 90：Analysis of circuit system response to periodic signals
Chapter 91：Analysis of general linear system response to periodic signals (1)
Chapter 92：Analysis of general linear system response to periodic signals (2)
Chapter 93：Frequency characteristics of linear systems
Chapter 94：System Frequency Curve Analysis Method
Chapter 95：Frequency domain analysis method of non-periodic signal response - from the perspective of signal superposition
Chapter 96：Comparison of response analysis methods for periodic signals and non-periodic signals
Chapter 97：The second view of frequency domain analysis method-directly from differential equations
Chapter 98：The third view of frequency domain analysis method—from the perspective of convolution integral
Chapter 99：A new solution method for system impulse response—Fourier transform method
Chapter 100：Comparison between frequency domain method and time domain method
Chapter 101：Filters and their classification
Chapter 102：Impulse response and step response of ILPF
Chapter 103：Analysis and discovery of ILPF step response—Four major revelations
Chapter 104：Definition and Judgment Method of Causal System
Chapter 105：Judging causality only from amplitude-frequency characteristics - Pellivina criterion
Chapter 106：Characteristics of physically realizable low-pass filters
Chapter 107：Several common types of low-pass filters
Chapter 108：The concept and meaning of modem
Chapter 109：AM waves and their spectrum
Chapter 110：AM wave modulation coefficient and power
Chapter 111：AM wave envelope demodulation principle
Chapter 112：The influence of amplitude modulation coefficient on amplitude modulated waves
Chapter 113：Principle of synchronous demodulation of amplitude modulated waves
Chapter 114：Suppressed carrier AM modulation and demodulation
Chapter 115：Principles of single sideband (and residual sideband) modulation and demodulation
Chapter 116：Principles of pulse amplitude modulation and demodulation
Chapter 117：Frequency division multiplexing and time division multiplexing of channels
Chapter 118：Causes of distortion and conditions for non-distortion
Chapter 119：Conditions for linear systems to transmit signals without distortion (2)
Chapter 120：Conditions for linear system to transmit AM waves without distortion
Chapter 121：Overview
Chapter 122：From Fourier transform to Laplace transform
Chapter 123：Derivation of the inverse Laplace transform
Chapter 124：Laplace transform pair
Chapter 125：Unilateral and Bilateral Laplace Transform
Chapter 126：The physical meaning of Laplace transform
Chapter 127：Definition of convergence interval
Chapter 128：Convergence region of one-sided Laplace transform
Chapter 129：Convergence region of bilateral Laplace transform
Chapter 130：The relationship between the existence condition of Fourier change and the convergence area of Laplace change
Chapter 131：Laplace transform of exponential signals
Chapter 132：Laplace Transform of Power Class Signals
Chapter 133：Laplace transform of impulse signals
Chapter 134：The idea of partial fraction decomposition method of inverse transformation
Chapter 135：Partial fraction decomposition method - case 1
Chapter 136：Partial fraction decomposition method - case 2
Chapter 137：Partial fraction decomposition method - case 3
Chapter 138：Residue calculation method of inverse transformation
Chapter 139：Example of calculating the inverse Laplace transform using the residue method
Chapter 140：Supplementary knowledge points on complex variable functions
Chapter 141：Calculation of remainders
Chapter 142：Things to note when calculating the inverse Laplace transform using the residue method
Chapter 143：Calculation method for residues that does not satisfy the inverse transformation of auxiliary covenant establishment
Chapter 144：Comparison of partial fraction decomposition method and residue method for solving inverse LT transform
Chapter 145：Extreme zero chart
Chapter 146：Linear characteristics & scale transformation characteristics
Chapter 147：Delay characteristics and Laplace transform of single-sided periodic signals
Chapter 148：Complex frequency shift characteristics
Chapter 149：Time domain differential characteristics
Chapter 150：Time domain integration characteristics
Chapter 151：Complex frequency domain calculus properties
Chapter 152：Parametric calculus properties
Chapter 153：Initial value theorem & final value theorem
Chapter 154：Convolution theorem & dual properties
Chapter 155：Solve the total response of the system from differential equations
Chapter 156：Solve the full response of the system from the circuit
Chapter 157：LT analysis of zero state response
Chapter 158：Calculation of H(s)
Chapter 159：LT analysis method for zero input response
Chapter 160：The relationship between the response components
Chapter 161：Introduction to RLC response analysis
Chapter 162：Definition and calculation of bilateral LT
Chapter 163：LT calculation of left signal
Chapter 164：LT calculation for bilateral signals
Chapter 165：partial fraction decomposition method
Chapter 166：Residue method
Chapter 167：Comparison of unilateral and bilateral LT calculations
Chapter 168：LT analysis method of linear system response to bilateral signals
Chapter 169：Analog block diagram and its basic units
Chapter 170：Block diagram corresponding to a simple differential equation
Chapter 171：Block diagram corresponding to a general form of differential equation
Chapter 172：System block diagram series and parallel implementation approach
Chapter 173：System simulation block diagram and simulation computer
Chapter 174：Introduction to flow graphs
Chapter 175：System functions and their physical meaning
Chapter 176：System frequency characteristics
Chapter 177：complex trajectory
Chapter 178：Extreme zero chart
Chapter 179：Characteristics of extremely zero graphs
Chapter 180：The relationship between the pole zero diagram and the zero input response of the system
Chapter 181：Extreme Zero Diagram and System Frequency Response
Chapter 182：All-pass system and minimum phase system
Chapter 183：Difficulties in expressing conventional frequency characteristic curves
Chapter 184：Bode plot of the system
Chapter 185：A brief introduction to the system Porter diagram method
Chapter 186：Bode plot of a single zero (pole) point system
Chapter 187：Synthesis of System Bode Plot
Chapter 188：Definition of system stability
Chapter 189：Necessary and sufficient conditions for system stability
Chapter 190：Extremes and Stability
Chapter 191：RH criterion (1)
Chapter 192：RH criterion (2)
Chapter 193：RH criterion (3)
Chapter 194：RH criterion (4)
Chapter 195：Feedback systems and their stability
Chapter 196：Introduction to Feedback Systems and Cybernetics
Chapter 197：How to transition from continuous to discrete
Chapter 198：Discrete Time Signals and Systems
Chapter 199：The relationship between continuous signals and discrete signals
Chapter 200：Representation of discrete signals
Chapter 201：Typical discrete time signals
Chapter 202：Simple processing of discrete time signals
Chapter 203：Linear shift invariant discrete time system
Chapter 204：ideal sampling
Chapter 205：Nyquist sampling theorem
Chapter 206：Sampling and recovery in actual projects
Chapter 207：difference equation
Chapter 208：Discrete time system block diagram
Chapter 209：Overview
Chapter 210：difference operator
Chapter 211：Zero input response solution
Chapter 212：Characteristic roots and stability
Chapter 213：Convolution and solution method for zero state response
Chapter 214：Calculation of convolution sum
Chapter 215：Properties of convolution sum
Chapter 216：Solution of h(k) (1)
Chapter 217：Solution of h(k)(2)
Chapter 218：Solution of h(k) - Example (3)
Chapter 219：Solution for full response (1)
Chapter 220：Solution for full response (2)
Chapter 221：Comparison of continuous and discrete time domain methods
Chapter 222：Overview of Transform Domain Analysis
Chapter 223：Export of Z transform
Chapter 224：Discussion of F(z)
Chapter 225：Unilateral and bilateral ZT
Chapter 226：Convergence region of Z transform
Chapter 227：Convergence region of ZT for finite-length signals
Chapter 228：The convergence area of ZT of the signal on the right
Chapter 229：The convergence area of ZT of the left signal
Chapter 230：Convergence area of ZT for bilateral signals
Chapter 231：ZT of common signals
Chapter 232：Calculation of ZT of the left signal
Chapter 233：Calculation of ZT for bilateral signals
Chapter 234：Linear & increasing order properties
Chapter 235：Decreasing order property
Chapter 236：Shifting properties of bilateral ZT
Chapter 237：Z-domain scale transformation & differential characteristics
Chapter 238：Convolution & initial and final value characteristics
Chapter 239：long division
Chapter 240：partial fraction expansion method
Chapter 241：Bilateral ZT inverse transform calculation
Chapter 242：Residue method (1)
Chapter 243：Residue method (2)
Chapter 244：The relationship between the sampling signal LT and the sequence ZT
Chapter 245：The relationship between the continuous signal LT and its corresponding sampling signal ZT
Chapter 246：Z-transform analysis method solution idea
Chapter 247：ZT solution for zero input response
Chapter 248：ZT solution for zero state response
Chapter 249：Synthesis of zero input and zero state response
Chapter 250：Full response one-time ZT solution method
Chapter 251：Discrete system stability determination (1)
Chapter 252：Discrete system stability determination (2)
Chapter 253：Implementation of H(z)
Chapter 254：Classification of digital filters
Chapter 255：Overview
Chapter 256：DTFT
Chapter 257：spectrum of a discrete signal
Chapter 258：DTFT of DC and sinusoidal signals
Chapter 259：DFS
Chapter 260：DTFT properties
Chapter 261：frequency domain analysis
Chapter 262：Frequency response of discrete systems
Chapter 263：Continuous vs. Discrete Comparison (1)
Chapter 264：Continuous vs. Discrete Comparison (2)
Chapter 265：Shortcomings of existing methods
Chapter 266：Advantages of the state equation representation of the system
Chapter 267：Equation of state
Chapter 268：Output equation
Chapter 269：Linear system state equation description method
Chapter 270：Equation of state in phase variable form
Chapter 271：Equation of state in diagonal form
Chapter 272：Diversity of Equations of State
Chapter 273：Equations of state for discrete time systems
Chapter 274：Selection of state variables in electrical systems
Chapter 275：Establishment of state equation
Chapter 276：Creation of output equations
Chapter 277：Another example
Chapter 278：LT Analysis of State Equation
Chapter 279：Solving the output equation
Chapter 280：Transfer function matrix & system natural frequency
Chapter 281：Characteristic roots of A matrix and system stability
Chapter 282：state transition matrix
Chapter 283：Controllability
Chapter 284：Observability
Chapter 285：Euler method
Chapter 286：Runge Kutafa
Chapter 287：Numerical analysis of nonlinear systems

Introduction

keywords： Signals and Systems Southeast University Mengqiao

Through the study of this course, students should be able to master the basic theories and methods of signal analysis, master various description methods of linear non-time-varying systems, master the time domain and frequency domain analysis methods of linear non-time-varying systems, and master relevant Some important conclusions in engineering applications such as system stability, frequency response, and causality. At the same time, through the study of this course, students' ability to analyze problems and use the knowledge they have learned to solve problems should also be improved on the original basis. Through the study of this course, students can lay a good foundation for further study of signal processing, network theory, communication theory, control theory and other courses in the future.

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