Page 154 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 31 LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS

SYSTEM FUNCTION

3.23. Find the system function H(s) and the impulse response h(t) of the RC circuit in Fig.
1-32 (Prob. 1.32).

(a) Let

In this case, the RC circuit is described by [Eq. (1.105)]

Taking the Laplace transform of the above equation, we obtain

Hence, by Eq. (3.37) the system function H(s) is

Since the system is causal, taking the inverse Laplace transform of H(s), the impulse
response h(t ) is

(b) Let

In this case, the RC circuit is described by [Eq. (1.107)l

Taking the Laplace transform of the above equation, we have

1
or (s + &)Y(S) = Rsx(s)

Hence, the system function H(s) is