4.δ函数的筛分性 f(s(dt =f(o 8(t)dt=f(O) f(0)() 同理有:f()6(t-t)dt=f(t) f()在t处连续 f() f(0) oo 例 (sint +t) (t-dt 0 =SIn十 6626
4. 函数的筛分性 − f ( t ) ( t ) d t ( ) ( ) d ( ) 0 0 f t t − t t = f t − 同理有： ) d 6 (sin t t ) ( t t − + − f(0) ( t) 1.02 2 6 1 6 6 = sin + = + = = f ( 0 ) ( t ) d t = f ( 0 ) − 例 t ( t) (1)0 f( t) f(0) * f( t) 在 t0 处连续
例2.脉冲序列分析 1.RC电路在单个脉冲作用的响应 R LL.=0 十 十 t<0 R C 1(0<t<T 0<<Tun1(t)=ua(∞)+u1(0+)-u1(∞)le le Rc u1(0+)=u1(0)=0VLa1(∞)=1J τ=RC u1()=1-g"c1,t>0 R ( t=o RC V t>0 i1(1)=e"CA,t>0 R
例2. 脉冲序列分析 1. RC电路在单个脉冲作用的响应 R C us uR uc i 1 0 T t us u 1 (0 t T) s = us = 0 0 t t T 1. 0<t<T RC t c c c c u t u u u e − + ( ) = () + [ (0 ) − ()] 1 1 1 1 uc1 (0 ) = uc1 (0 ) = 0V + − uc1 () = 1V = RC 1 ( ) = 1− , 0 − u t e V t RC t c 1 ( ) = , 0 − u t e V t RC t R , 0 1 ( ) 1 = − e A t R i t RC t