信号与系统课件2013-13-2.ppt

Chapter 10 Discrete-time Linear Time-invariant System Introduction Recall two important properties: Why do we research LTI systems? Test for time invariance Linearity Why emphasizing LTI systems? 离散LTI系统占有十分重要的地位，这是因为: 许多的物理系统都可按照LTI系统建模。例如，大多数数字滤波器。 我们可以解出描写连续和离散的LTI模型的方程解。 通过LTI系统的分析和设计，可以得到很多关于系统的信息。 10 discrete-time linear time-invariant system Impulse representation of discrete-time signals; Convolution for discrete-time LTI System; Properties of DT LTI systems; Difference equation models; Terms in the natural response; Block diagrams System response for complex-exponential inputs. 10.1 Impulse representation of discrete-time signals Recall impulse function; Relationship between common signal and impulse function. Discrete-time signals Review of unit impulse function Relationship for common signal and impulse function 10 discrete-time linear time-invariant system Impulse representation of discrete-time signals; Convolution for discrete-time LTI System; Properties of DT LTI systems; Difference equation models; Terms in the natural response; Block diagrams System response for complex-exponential inputs. 10.2 Convolution for discrete-time LTI System Sum of impulse response Definition of Convolution Sum 卷积和揭示，一个LTI离散系统的冲激响应h[n]，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，就可以利用卷积和求取任意输入信号作用下的系统响应。 Additional properties of convolution sum Convolution for unit impulse: y[n]=?[n]*h[n]=h[n]; y[n-n0]=?[n -n0]*h[n]=?[n]*h[n-n0]=h[n-n0]; g[n]=?[n]*g[n]; g[n-n0] = ?[n -n0]*g[n]=?[n]*g[n-n0]; Difference between convolution and multiplication! 卷积和的另外一个例子 FIR and IIR system FIR system, finite impulse response; IIR system, infinite impulse response; Example 10.3; Example 10.4. 10.2 Convolution for discrete-time LTI System Properties of convolution Three properties of convolution Commutative property, figure 10.7; Associative property, figure 10.8; Distributive property, figure 10.9. Example 10.5 10.3 Properties of discrete-time LTI systems 无记忆系统(Memoryless Systems) 可逆性(Invertibili