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A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal to
- a)2RX (τ) + RX (τ - T0) - RX (τ + T0)
- b)2RX (τ) - RX (τ - T0) - RX (τ + T0)
- c)2RX (τ) + 2RX (τ - 2T0)
- d)2RX (τ) - 2RX (τ - 2T0)
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A wide sense stationary random process X(t) passes through the LTI sys...
1. Autocorrelation function for a process Y(t) is given by Rx(τ) = E[Y(t) Y(t + τ)].
2 . For a WSS process Shifting does not affect the autocorrelation function.
Application:
We have Y(t) = X(t) – X(t – T0)
Now Rx(τ) = E[Y(t) Y(t + τ)]
RY(τ) = E[[(X(t) - X(t - T0)][X (t + τ) = X(t + τ - T0)]]
2 . For a WSS process Shifting does not affect the autocorrelation function.
Application:
We have Y(t) = X(t) – X(t – T0)
Now Rx(τ) = E[Y(t) Y(t + τ)]
RY(τ) = E[[(X(t) - X(t - T0)][X (t + τ) = X(t + τ - T0)]]
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A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. Can you explain this answer?
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A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. 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 A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. 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 A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. Can you explain this answer?.
A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. 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 A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. 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 A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is RX(τ), then the autocorrelation function RY(τ) of the output Y(t) is equal toa)2RX(τ) + RX(τ - T0) - RX(τ + T0)b)2RX(τ) - RX(τ - T0) - RX(τ + T0)c)2RX(τ) + 2RX(τ - 2T0)d)2RX(τ) - 2RX(τ - 2T0)Correct answer is option 'B'. Can you explain this answer?.
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