GATE 2014 EC (EC2) – Question 61
A real stationary process X(t) has PSD $S_X(f)=1/W$ for $|f|\le W$, and zero otherwise. Find $E[\pi X(t)X(t-1/(4W))]$.
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Correct answer: 3.9 to 4.1
Explanation
By Wiener-Khinchin, RX(τ)=∫₋Wᵂ(1/W)e^(j2πfτ)df=sin(2πWτ)/(πWτ). At τ=1/(4W), this becomes1/(π/4)=4/π. Multiplying by the supplied factorπ gives **4**. The PSD area RX(0)=2is a useful normalization check.