Question

If the response of LTI continuous time system to unit step input is (\(\frac{1}{2} –  \frac{1}{2} e^{-2t}\)), the impulse response of the system is _______________

(a) (\(\frac{1}{2} –  \frac{1}{2} e^{-2t}\))

(b) e^-2t

(c) (1-e^-2t)

(d) Constant

The question was asked during an online interview.

I would like to ask this question from Characterization and Nature of Systems in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (b) e^-2t

For explanation I would say: We know that, impulse response is given by \(\frac{d [step \,response]}{dt}\)

Step response = (\(\frac{1}{2} –  \frac{1}{2} e^{-2t}\))

∴ Impulse response = \(\frac{d (\frac{1}{2} –  \frac{1}{2} e^{-2t})}{dt}\)

= e^-2t.