Pulse Response

Abstract

The pulse function shares some similarities to the unit step function; after all it is a unit step function but of finite width; that is instead of input energy pouring for all time, it ceases after some time—the pulse width. The pulse function also has some resemblance to the impulse function; after all if we make the pulse width very narrow and pulse height very tall we do approach an impulse function! As can be seen the pulse function is of very much relevance. It samples the system such that the system is strongly driven, but releases control after some time such that the system proceeds to the relaxation stage. Also, the pulse function paves the way for the very much relevant and important function of causal periodic pulse which will be treated next. With all this in background we are ready to figure the pulse response by starting with the system transfer function, multiplying by the Laplace transform of the pulse which is (1 − e ^−Ts)/s (where T is pulse width), and lastly by finding the inverse transform of the resulting function. Again we illustrate the process of figuring the pulse response on various RLC circuits, including feedback and in the process study some of the interesting observations of such circuits.