RC System

Consider a RC system consisting of a resistor and a capacitor. We have to find out what the response of this system is to the unit impulse

First let us understand the response to

If the input is the unit step function u(t) then the output of the system will be . Let us call this output of the system S(t). Hence we can say that the response to will be given as follows:

Now as the response of will be equal to h(t)

Taking limit as on both sides and using we get

By the sifting property we get  

Hence if we are given the unit step response u(t) we have been able to calculate the continuous impulse response of the system. Next we shall see how we can get the unit step response from the impulse response of the same system.