Concept:
ACF is defined as:
Rx(τ) = E[x(t) x(t + τ)] = E[x(t) x(t - τ)]
Properties of ACF:
1. Rx(-τ) = Rx (τ)
2. Rx (0) = E [x2(t)] = Power of x(t)
Calculation:
Given:
x(t) = 3 V(t) – 8, Rv(τ) = 4e-5|τ|
E [V(t)] = 0
We know that,
Power of x(t) = E[x2(t)]
= E[9V2(t) + 64 – 48 E[V(t)]]
= 9E [V2(t)] + 64 – 48 E[V(t)]
Now,
E[V2(t)] = Rv(0) = 4
So,
Power of x(t) = (9 × 4) + 64 – 0
Power of x(t) = 100