电子科大讲义课堂信号.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Chapter 2,Linear Time-invariant Systems,Chapter 2 LTI Systems,1,0 2 4 t,1,L,Consider an linear time-invariant system,Example 1,0 2 t,1,0 1 2 t,1,L,0 2 4 t,1,-1,Chapter 2 LTI Systems,2,2.1 Discrete-time LTI Systems:The Convolution Sum,（卷积和）,1.The Representation of Discrete-Time Signals,in Terms of impulses,Sifting Property,离散时间信号的冲激表示,2.The Unit Impulse Responses,单位冲激响应,Chapter 2 LTI Systems,3,Convolution-Sum（卷积和）,系统在n时刻的输出包含所有时刻输入脉冲的影响,k时刻的脉冲在n时刻的响应,3.卷积和的计算,图解法,普通乘法,因果序列或有限长度序列之间的卷积,Chapter 2 LTI Systems,4,Example 3,Determine,Solution,3142hn,215xn,1552010,3142,6284,6524132210,y0,y1,y2,y3,y4,y5,yn=6,5,24,13,22,10 n=0,1,2,3,4,5,Chapter 2 LTI Systems,5,多项式算法（适用于有限长度序列）,yn=6,5,24,13,22,10 n=0,1,2,3,4,5,利用多项式算法求卷积和的逆运算,已知 yn 、hn xn,已知 yn 、xn hn,Chapter 2 LTI Systems,6,Example 4,Determine xn,yn=6,5,24,13,22,10 n=0,1,2,3,4,5,y(t),0,Chapter 2 LTI Systems,7,2.2 Continuous-Time LTI Systems:The Convolution Integral,（卷积积分）,1.The Representation of Continuous-Time Signals,in Terms of impulses,Sifting Property,Chapter 2 LTI Systems,Convolution Integral,卷积积分,时刻的冲激,t 时刻的响应,2.The Convolution Integral,8,2.3 卷积的计算,一 由定义计算积分,例2.6,Chapter 2 LTI Systems,二 图解法,9,Chapter 2 LTI Systems,例2.7 求下列两信号的卷积,其余t,其余t,解：,10,Chapter 2 LTI Systems,11,2.3 Properties of LTI Systems,LTI系统的特性可由单位冲激响应完全描述,2.3.1 Properties of Convolution Integral and Convolution Sum,1.The Commutative Property(交换律）,Chapter 2 LTI Systems,12,2.The Distributive Property (分配律）,Chapter 2 LTI Systems,13,Commutative,Property,Associative Property,3.The Associative Property (结合律）,Chapter 2 LTI Systems,14,4.含有冲激的卷积,Chapter 2 LTI Systems,15,5.卷积的微分、积分性质,微分,积分,Chapter 2 LTI Systems,16,Example,otherwise,otherwise,Solution 1,0 1 2 3 t,0 1 2 3 t,Integral,Chapter 2 LTI Systems,17,Solution 2,0 1 2 3 t,0 1 2 3 t,Chapter 2 LTI Systems,18,Example,Consider the convolution of the two signals,(1),(1),0 t,-1 0 1 t,-2 -1 0 1 2 t,-2,-2 -1 0 1 2 t,-2,(-2),19,6 几种典型系统,恒等系统,微分器,积分器,延迟器,累加器,Chapter 2 LTI Systems,20,2.3.4 LTI Systems with and without Memory,1.Discrete-time System,It is memoryless,An LTI system without memory,2.Continuous-time System,An LTI system without memory,Chapter 2 LTI Systems,21,2.3.5 Invertibility of LTI Systems,LTI系统的可逆性,System,Inverse System,identity system(恒等系统）,Chapter 2 LTI Systems,22,2.3.6 Causality for LTI Systems,LTI系统的因果性,1.Discrete-time System,与n时刻以后输入有关,Causal,system,2.Continuous-time System,Causal,system,Chapter 2 LTI Systems,23,2.3.7 Stability for LTI Systems (稳定性）,1.Discrete-time System,Stable,System,absolutely,Summable,绝对可加,2.Continuous-time System,Stable,System,absolutely,Integrable,绝对可积,Chapter 2 LTI Systems,24,2.3.8 The Unit Step Response of an LTI Systems,LTI系统的单位阶跃响应,Discrete-time System,Continuous-time System,Unit Step,Response,Unit Step,Response,Chapter 2 LTI Systems,25,作业：,2.1 2.5 2.10,2.7 2.11 2.12,2.22(a)(c),2.20 2.23 2.40 2.46 2.47,Chapter 2 LTI Systems,26,2.5,Determine the value of N.,Chapter 2 LTI Systems,27,2.7 A linear system S has the relationship,between its input and output,(c)S is time-varying.,Chapter 2 LTI Systems,28,Chapter 2 LTI Systems,29,2.10 Suppose that,(a)Determine,(b)If contains only three discontinuities,what is the value of a?,Solution：,0 a 1 1+a t,Chapter 2 LTI Systems,30,2.12 Let,Show that for,Determine the value of A.,Chapter 2 LTI Systems,31,2.20.Evaluate the following integrals:,Chapter 2 LTI Systems,32,2.22(c),one period of,Chapter 2 LTI Systems,33,2.23,Determine and sketch for the following value of T:,(a)T=4 (b)T=2 (c)T=3/2 (d)T=1,Chapter 2 LTI Systems,34,0 t,(c)T=3/2,(a)T=4,-5 -4 -3 -1 0 1 3 5 t,(d)T=1,0 t,-3 -1 0 1 3 t,(b)T=2,Chapter 2 LTI Systems,35,2.40 (a)an LTI system:,What is the impulse response for this system?,(b)Determine the response of,Chapter 2 LTI Systems,36,2.46 Consider an LTI system S and a signal,and,If,Determine the impulse response of S.,Chapter 2 LTI Systems,37,2.47 An LTI system with impulse response,0 2 t,In each of these cases,determine,whether or not we have enough,Information to determine the output,Chapter 2 LTI Systems,We have not enough information to determine the output,38,2.24,Find the impulse response,Find the response of the,overall system to the input,Chapter 2 LTI Systems,39,例1 已知一LTI系统的单位,冲激响应 如图所示，,若输入信号为单位阶跃,信号 ，试求其输出,Chapter 2 LTI Systems,40,例2,已知离散时间信号 ，要求：,1.画出 的波形；,2.求出满足 的序列。

Chapter 2 LTI Systems,41,图1,例 某离散时间LTI系统的系统框图如图1所示，已知两个子系统,的单位冲激响应分别为,若输入信号 ，试求系统的输出,Chapter 2 LTI Systems,42,。