Signals and Systems

5.2 IMPULSE RESPONSE AND TRANSFER FUNCTION

The impulse function has been already discussed in Chapter 1. In Chapter 5, we have derived the Laplace transform of impulse function [δ(t)] which is unity.

From Fig. 5.1(b), we can write Eq. (5.1) as follows:

 

 

The response C(s) can be found in terms of transfer function from Eq. (5.2). Here G(s) and R(s) are Laplace transforms of g(t) and r(t) respectively. Therefore, the response of any input r(t) can be found out. Eq. (5.2) represents a general equation and it is valid for any input.

Let us take the impulse input

 

r(t) = δ (t)

 

∴                                R(s) = LT[δ(t)] = 1          (5.3) ...