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)= \{ \table 1, {|f|} \leq \frac{1}{2} \Hz; 0, {|f|} > \frac{1}{2} \Hz This is as shown in Figure (b). The output of the lowpass filter is Y(t). Let E be the expectation operator. Consider the following statements: I. E(X(t)) = E(Y(t)) II. E(X 2 (t)) = E(Y 2 (t)) III. E(Y 2 (t)) = 2 Select the correct option:

Correct Answer is : only I is true

GATE Electronics and Communications (EC) 2017 Shift 1 Solved Paper

Question : 61 of 65

Marks: +1, -0

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)= \{ \table 1, {|f|} ≤ \;{1}/{2} \Hz; 0, {|f|} > {1}/{2} \Hz

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

Let E be the expectation operator. Consider the following statements:
I. E(X(t)) = E(Y(t))
II. E(X²(t)) = E(Y²(t))
III. E(Y²(t)) = 2
Select the correct option:

only I is true
only II and III are true
only I and II are true
only I and III are true

Validate

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