# Relationship between unit step response and impulse of a system

This answer applies to linear continuous systems; for discrete systems, it is easy to generalize the same properties, working with sums instead of integrals and. Linear systems can be characterised in terms of the output response to an impulse or a step input. The impulse input occurs over an infinitesimally short interval. In the given question, system is assumed to be causal, input is unit step . Instead, the step response is the convolution of unit impulse response with the step.

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