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

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

Let E be the expectation operator and 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:
  • a)
    only I is true
  • b)
    only II and III are true
  • c)
    only I and II are true
  • d)
    only I and III are true
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let X(t) be a wide sense stationary random process with the power spec...


Since DC components in same in Sx (f) and Sy (f)
⇒ E[x(t)] = E[y(t)]
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Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency responseAs shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator and consider the following statements.I. E (X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:a)only I is trueb)only II and III are truec)only I and II are trued)only I and III are trueCorrect answer is option 'A'. Can you explain this answer?
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Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency responseAs shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator and consider the following statements.I. E (X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:a)only I is trueb)only II and III are truec)only I and II are trued)only I and III are trueCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency responseAs shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator and consider the following statements.I. E (X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:a)only I is trueb)only II and III are truec)only I and II are trued)only I and III are trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency responseAs shown in Figure (b). The output of the lowpass filter is Y(t).Let E be the expectation operator and consider the following statements.I. E (X(t)) = E(Y(t))II. E(X2(t)) = E(Y2(t))III. E(Y2(t)) = 2Select the correct option:a)only I is trueb)only II and III are truec)only I and II are trued)only I and III are trueCorrect answer is option 'A'. Can you explain this answer?.
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