三、卷积和的性质1.满足乘法三律：(1)交换律（2)分配律（3)结合律2. f(k)* (k)=f (k) , f(k)* 8 (k- kO)=f(k - k0)K3. f(k)*ε (k) =Zf(i)i=-004. f1 (k - k1)* f2(k - k2)=f (k - k1 - k2)5.△[f, (k)*f,(k)=△f, (k)*f, (k)=f, (k)*△f, (k)第6页
第 6 页 三、卷积和的性质 1.满足乘法三律：(1)交换律(2)分配律(3)结合律. 2. f(k)*δ(k)=f(k) ，f(k)*δ(k–k0)=f(k–k0) 3. f(k)*ε(k) = k i f (i) 4. f1(k–k1)* f2(k–k2) =f(k–k1–k2) 5. △[f1(k)*f2(k)]=△f1(k)*f2(k)=f1(k)*△f2(k)
ε(t)* ε (t)=tε(t)ε（t+a)*ε（t+b)=(t+a+bε（t+a+bc(k)*c(k) = (k+1)c(k)ε(k+a)*ε(k+b)=(k+a+b+1)(k+a+b)第了贵
第 7 页 第 7 页 ε(t)*ε(t)=tε(t) ε(t+a)*ε(t+b)=(t+a+b)ε(t+a+b) ε(k)*ε(k) = (k+1)ε(k) ε(k+a)*ε(k+b)=(k+a+b+1)ε(k+a+b)