Question

A causal LTI filter has the frequency response $H\left(j\omega \right)$ as shown below,

For the input signal $x\left(t\right)=e^{-jt}$, output will be

• A. $-2j{e}^{-jt}$
• B. $-4\pi j{e}^{-jt}$
• C. $2j{e}^{-jt}$
• D. $4\pi j{e}^{-jt}$

Answer 1

The correct option is C $2j{e}^{-jt}$

$H\left(j\omega \right)=-2j\omega$

$Y\left(j\omega \right)=X\left(j\omega \right)H\left(j\omega \right)$

$=-2j\omega X\left(\omega \right)$

$y\left(t\right)=\frac{-2dx\left(t\right)}{dt}=2j{e}^{-jt}$

$\because x\left(t\right)=e^{-jt}\left(given\right)$