Signals and Systems

4.12 RELATION BETWEEN STEP RESPONSE AND IMPULSE RESPONSE

Let input to the network shown in Fig. 4.12 be v_i (t), let the output or response of the network be v₀(t). The Laplace transform of v_i (t) and v₀ (t) be V_i (s) and V₀(s) respectively. V_s

 

 

Fig. 4.12 Impulse response of a network

 

The ratio of Laplace transform of output to that of input putting initial conditions to zero is known as transfer function.

 

 

Taking its inverse Laplace transform, we have

 

 

If v_i(t) be an impulse function, i.e. V_i(t) = δ (t), the Laplace transform of ...