I'm trying to understand impulse and unit step responses, but I'm not sure if my understanding is correct. In general, are the following statements true:
a) The impulse response for a system $x(t) \mapsto y(t)$ is $y(t)$ when $x(t) = \delta(t)$ where $\delta$ is the Dirac delta, and
b) The unit step response for a system $x(t) \mapsto y(t)$ is $y(t)$ when $x(t) = u(t)$ where $u$ is the unit step (Heaviside step function)