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Electric Generator

Given xt is a...

Question

Given x(t) is an Ergodic Random Process (ERP), with autocorrelation function as below:

The AC Power of x(t)______(in watt) is
6

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Solution

The correct option is A 6
For Ergobic RP:
$L i m_{τ \to \infty} R_{x} (τ) = m_{1}^{2} = D C P o w e r = 2 w a t t$

and $R_{X} (0) = E [X^{2} (t)] = m_{2} = t o t a l p o w e r = 8 w a t t$

$R_{x} (0) - R_{x} (\infty) = m_{2} - m_{1}^{2} = V a r i a n c e = A C p o w e r$

$= 8 - 2 = 6 w a t t$

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