unit impulse response

Ask

For a first order system having transfer function ${1\over(1+sT)}$, the unit impulse response is

(a) $e^{-t/T}$

(b) $Te^{-t/T}$

(c) ${1\over T} e^{-t/T}$

(d) $T^2 e^{-t/T}$

Answer is ( c )

Concept

Solution:In General , the Transfer Function of a system is described in s-domain or z-domain. 

For any given system function / transfer function - The Unit Impulse Response is TIME DOMAIN system RESPONSE

          $\therefore T.F = {1\over(1+sT)}$
                               $= {1/T\over 1/T+s}$

$= \frac{1}{T}\left(\frac{1}{s+1}\right)$

$= {1\over T} e^{-t/T}$