电子科大信号与系统课件 第二章.pptVIP

Signals and Systems Chapter 2 Linear Time-Invariant Systems Liu Ke, School of Automation Engineering 2.0 Introduction Two important properties in chapter 1 The application of Linear and Time-invariant system The Contents Of Chapter 2 Discrete-Time LTI System:The Convolution Sum √ Continuous-Time LTI System:The Convolution Integral √ Properties of linear time-invariant systems √ Causal LTI systems Described by Differential and Difference Equations √ Singularity functions Conclusion Convolution Sum Convolution Integral Properties of linear time-invariant systems Differential and Difference Equation Singularity functions 2.3.4 LTI Systems with and without memory Discrete-time system without memory Continuous-time system without memory Example: y(t)=x(t)+x(t-1) 2.3.5 Invertibility of LTI System h(t) h1(t) Example 2.11 Example 2.12 2.3.6 Causality of LTI System causal for a linear system ??initial rest Causal Signals The signal which is zero if n0 or t0 Causality of an LTI system is equivalent to its impulse response being a causal signal. Initial rest(初始松弛) 2.3.7 Stability of LTI System Example 2.13 2.3.8 The Unit Step Response of LTI System Relationship of the impulse response and the unit step response The unit step response can also used to characterize an LTI system.Since we can calculate the unit impulse response from it . 2.4 Causal LTI Systems Described Differential And Difference Equations Linear constant-coefficient differential equation RC circuit、Automobile Linear constant-coefficient difference equation saving in bank account、simulate 2.4.1 Linear Constant-Coefficient Differential Equation Implicit Specification Obtain an explicit expression solve a differential equation one or more auxiliary condition different auxiliary condition lead to different relationship between the input and the output Example 2.14 Homogeneous solution (natural response) Particular solution (forced response) Auxiliary condition (initial rest) Conclusion Th