信号与系统课件2013-3.ppt

Chapter 3 Continuous-time Linear Time-invariant System (LTI) Introduction Impulse representation of continuous-time signals Convolution for continuous-time LTI systems Properties of convolution Property of continuous time LTI systems Differential-Equation models Terms in the natural response System response for complex-exponential inputs * Block diagrams Introduction Introduction Recall two important properties: Why do we research LTI systems? The reasons for emphasizing LTI systems 许多的物理系统可以用LTI模型来分析和研究。 LTI系统的分析方法已经形成了完整的、严密的体系，可以用数学方法解出描写连续和离散的LTI模型的方程解。对于非LTI的系统，通常没有一定的数学求解方法。 通过LTI系统的分析和设计，可以得到很多关于系统的信息。用一个LTI模型来替代这个物理系统，从而具有了一个原始模型。 有时可以利用LTI系统的线性性质求解系统的响应。 Chapter 3 Continuous-time Linear Time-invariant System (LTI) Introduction Impulse representation of continuous-time signals Convolution for continuous-time LTI systems Properties of convolution Property of continuous time LTI systems Differential-Equation models Terms in the natural response System response for complex-exponential inputs * Block diagrams 3.1 Impulse representation of continuous-time signals Definition of unit impulse function 冲激函数的性质，table 2－3 偶函数 微积分 筛选 尺度变换 3.1 Impulse representation of continuous-time signals Relationship for common signal and impulse function 3.1 Impulse representation of continuous-time signals Physical meaning of this relationship (1) Physical meaning of this relationship (2) Conclusion: 3.2 Convolution for Continuous-time LTI System Impulse response Sum of impulse response (1) Sum of impulse response (2) 3.2 Convolution for Continuous-time LTI System Definition of Convolution Integral 卷积积分揭示，一个LTI连续系统的冲激响应h(t)，可以完整地描述了系统的输入输出关系。如果冲激响应已知，就可以利用卷积（3-14）求取任意输入信号作用下的系统响应。 One property 3.2 Convolution for Continuous-time LTI System Additional properties of convolution integral y(t)=?(t)*h(t)=h(t); y(t-t0)=?(t -t0)*h(t)=?(t)*h(t-t0)=h(t-t0); g(t)=?(t)*g(t); g(t-t0) = ?(t -t0)*g(t)=?(t)*g(t-t0); Difference between convolution and multipli