The unit impulse response of a system is given by C (t)

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The unit impulse response of a system is given by C (t) = 0.5 e^–t/2. Its transfer function is—

1. 1/(s + 2)
2. 1/(1 + 2s)
3. 2/(1 + 2s)
4. 2/(s + 2)

Correct Option: B

Given C (t) = 0.5 e^{– t/2}
C (s) = 0·5 × 1/ (s + 1/2)

=	2 × 0.5	=	1
	2(s + 1)		2s + 1

If input, r (t) = δ (t) then, R (s) = 1
Transfer function,

H(s) =	C(s)	=	1
	R(s)		2s + 1