Official PYQ · 2017Set 1 · Q51Random ProcessesMCQ2 marks

GATE EC 2017 Set 1 Q51 — Random Processes

Let $X(t)$ be a wide sense stationary random process with the power spectral density $S_{X}(f)$ as shown in Figure (a), where $f$ is in Hertz $(Hz)$ . The random process $X(t)$ is input to an ideal lowpass filter with the frequency response

$H(f) = \begin{cases} 1, & \mid f \mid \leq \frac{1}{2} Hz \\ 0, &\mid f \mid > \frac{1}{2} Hz \end{cases}$

as shown in Figure(b).The output of the lowpass filter is $Y(t)$ .

Let $E$ be the expectation operator and consider the following statement:

$E(X(t))=E(Y(t))$
$E(X^{2}(t))=E(Y^{2}(t))$
$E(Y^{2}(t))=2$

Select the correct option:

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Answer: A

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Published 10 Oct 2026

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