Does the convolution $q(t) = q'(t)\circledast\theta(t)$ always holds? Why?, if not, What is needed?
Taking the bilateral Laplace transform we have
$$ Q(s) = (s Q(s))\frac 1s $$
so
$$ Q(s)=Q(s) $$
which is true for all $|q(t)|\le M e^{\alpha t}$
Does the convolution $q(t) = q'(t)\circledast\theta(t)$ always holds? Why?, if not, What is needed?
Taking the bilateral Laplace transform we have
$$ Q(s) = (s Q(s))\frac 1s $$
so
$$ Q(s)=Q(s) $$
which is true for all $|q(t)|\le M e^{\alpha t}$