卷积运算

gaohaikuo1

两大口诀
1,$\delta(t)$卷积类乘1

$f(t)*\delta(t) = f(t)$

$f(k)*\delta(k) = f(k)$

$f(k)*\epsilon(k) =\sum_{i = -\infty}^{k}f(i)$

2.卷积兄弟共天地

共天$f_1^{(n)}(t)*f_2(t) =f_1(t)*f_2^{(n)}(t)$

共地$f_1(t-t_0)*f_2(t) =f_1(t)*f_2(t-t_0)$

$f_1(k-k_0)*f_2(k) =f_1(k)*f_2(k-k_0)$