Question

A Narrow Band Random Process is given as $x\left(t\right)=p\left(t\right)cos{\omega }_{c}t-q\left(t\right)sin{\omega }_{c}t.$The auto correlation function of $p\left(t\right)is{R}_P\left(\tau \right)=4e^{-2\tau }$ and mean of p(t) = 1. Then,

• A. Power of x(t) = 4 watt
• B. AC value of x(t) = 2
• C. E[p(t). q(t)] = 0
• D. DC power of q(t) = 1 watt

Answer 1

Answer: (A), (C), (D)

DC power of q(t) = 1 watt

$Powerofx\left(t\right)=p\left(t\right)=q\left(t\right)=R_p\left(0\right)=4=MSQ$

$\Rightarrow m_x=m_p=m_q=1=\sqrt{D.C.Power}$

$\Rightarrow DCPower=1Watt$

$\Rightarrow ACPower={\sigma }^2=MSQ-m_x^2$

$=4-1^2$
= 3 watt
AC value $=\sqrt{3}$