Chapter 2 LTI SyStems 52.3. 1 Properties of Convolution Integral and Convolution Sum 1. The Commutative Property(交换律) x()*h()=h()+x(t) x[四]+hla]=h]*x] x*()= hlt)*x 11
11 Chapter 2 LTI Systems §2.3.1 Properties of Convolution Integral and Convolution Sum 1. The Commutative Property (交换律） xnhn= hn xn x(t)h(t) = h(t) x(t) x(t)h(t) h(t) x(t) h(t) x(t) h(t) x(t)
Chapter 2 LTI SyStems 2. The Distributive Property(分配律) x()*1()+h2()}=x()*h1()+x()*h2( x四*+2[=x*1团+x]*h2 h() A0.0三 h2() 12
12 Chapter 2 LTI Systems 2. The Distributive Property (分配律） xn h n h n xn h n xn h n 1 + 2 = 1 + 2 x(t) h (t) h (t) x(t) h (t) x(t) h (t) 1 + 2 = 1 + 2 x(t) y(t) h (t) h (t) 1 + 2 h (t) 1 x(t) h (t) 2 y(t)
Chapter 2 LTI SYStems 3. The Associative Property(结合律) {x()*h1(*h2()=x()*1()+h2( x小]*h[四*h四=x小*{[小*h2[ h(h() )=x( h()*h2() Commutative Propert x() 40)0三的A) Associative Property
13 Chapter 2 LTI Systems 3. The Associative Property (结合律） xnh1 nh2 n= xnh1 nh2 n x(t)h1 (t)h2 (t) = x(t)h1 (t)h2 (t) h (t) 1 x(t) h (t) 2 y(t) x(t) y(t) h (t) h (t) 1 2 x(t) y(t) h (t) h (t) 2 1 Commutative Property h (t) 1 x(t) h (t) 2 y(t) Associative Property
Chapter 2 LTI SyStems 4.含有冲激的卷积 x(t)*()=x() xIn sin=x ② 水 x(t-t)*(t-1)=y(-1-t2) 14
14 Chapter 2 LTI Systems 4. 含有冲激的卷积 ① x(t) (t) = x(t) ② y(t) = x(t)h(t) ( ) ( ) ( ) 1 2 1 2 x t −t h t −t = y t −t −t xn n= xn
Chapter 2 LTI SyStems 5.卷积的微分、积分性质 ①微分性质 y()=x()*h(t)=x()*h(t) ()=x(G)+h()=x(G)+h0 ②积分性质 p)(t)=x(t)+h()()=x()+h(t) y-()=xm()+h()=x(0)+hm()m>0 ③推广形式 y()=x()+h()=x()+h( )n0微分 n<0积分5
15 Chapter 2 LTI Systems 5. 卷积的微分、积分性质 ① 微分性质 ② 积分性质 y(t)= x(t)h(t)= x(t)h(t) ( ) ( ) ( ) ( ) ( ) ( ) ( ) y t x t h t x t h (t) n n n = = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 y t x t h t x t h t − − − = = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 m m m y t x t h t x t h t m − − − = = ③ 推广形式 ( ) ( ) ( ) ( ) ( ) ( ) ( ) y t x t h t x t h (t) n n n = = n>0 微分 n<0 积分