1. Index response of linear systems with localized constants

The indexical response of a system is the response s (t ) to the action e (t ) equal to the unit step (Heavyside step), which will be referred to here as ϒ (t ). This study makes it possible to obtain the response of a system to an ideal rectangular pulse by considering the difference between the responses to two steps separated by a time t _p . The index response is calculated using the Laplace transform: $e\left(t\right)=\Upsilon \left(t\right)\iff E\left(p\right)=\frac{1}{p}$