Question

The unit impulse response of a system is given as:
$C\left(t\right)=-4e^{-t}+6e^{-2t}$

The step response of the same system for $t\ge$0 is equal to

• A.
  $-3e^{-2t}+4e^{-t}-1$
• B.
  $-3e^{-2t}+4e^{-t}+1$
• C.
  $3e^{-2t}+4e^{-t}-1$
• D.
  $-3e^{-2t}-4e^{-t}-1$

Answer 1

The correct option is A

$-3e^{-2t}+4e^{-t}-1$
$\text{Impulse response =}-4e^{-t}\text{+ 6e}{}^{-2t}$

$\text{Step response =}{\int }_{-\infty }^t\text{C(t)dt}$

$={\int }_0^t-4e^{-t}dt+{\int }_0^{t}6e^{-2t}dt$

$=4e^{-t}-3e^{-2t}-1$

$\text{Hence, option (b) is correct}$