Question

The impulse response h(t) of an LTI system is given by, If a zero mean white Gaussian process with a two-sided power spectral density of 0.25 $\mu$W/Hz is applied as input to the above said LTI system, then the output noise power will be ____ $\mu$W

• A. 6

Answer 1

The correct option is A 6
Given that, $S_x\left(f\right)=0.25\mu W/Hz$

Output PSD, $S_Y\left(f\right)=S_X\left(f\right)|H\left(f\right){|}^2$

Output power, $P_Y={\int }_{-\infty }^{\infty }{S}_Y\left(f\right)df={\int }_{-\infty }^{\infty }{S}_X\left(f\right)|H\left(f\right){|}^{2}df$

$=0.25{\int }_{-\infty }^{\infty }|H\left(f\right){|}^{2}df=0.25{\int }_{-\infty }^{\infty }|h\left(t\right){|}^{2}dt$

$=0.25{\int }_{-3}^3(2{)}^{2}dt=(0.25\left)\right(24)\mu W=6\mu W$