例1证明 f()+[2()+3(O)]1(t)*2()+f1(1)*3(1) 证根据卷积的定义 f()*[力2()+f3(t f(olfa(t-t)+f(t-t]dt + + f()(-)dz+f(r)/3(t-)dz =f1(t)*2(t)+f1(1)*方3(1)9 例1 证明 f1 (t)*[f2 (t)+f3 (t)]=f1 (t)*f2 (t)+f1 (t)*f3 (t) 证 根据卷积的定义 ( ) ( ) ( ) ( ). ( ) ( )d ( ) ( )d ( )[ ( ) ( )]d ( ) [ ( ) ( )] 1 2 1 3 1 2 1 3 1 2 3 1 2 3 f t f t f t f t f f t f f t f f t f t f t f t f t =  +  = − + − = − + −  + =    + − + − + −          