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Signals and Systems by Smarajit Ghosh

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4.12 RELATION BETWEEN STEP RESPONSE AND IMPULSE RESPONSE

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

 

Impulse response of a network

 

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.

 

Image

 

Taking its inverse Laplace transform, we have

 

 

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

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