GATE EC 2014 Set 3 — Question 59
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Communications → Random Processes → Autocorrelation & PSD
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Question
Let be a wide sense stationary (WSS) random process with power spectral density . If is the process defined as , the power spectral density is
Correct answer
(C) S_Y(f) = (1)/(2) S_X ((f)/(2))
Solution
Given . For a wide sense stationary (WSS) process, the autocorrelation function of is:
.The power spectral density (PSD) is the Fourier transform of the autocorrelation function:
.Using the scaling property of the Fourier transform, , where :
.Note that the time shift in the process does not affect the autocorrelation of a WSS process, and consequently, it does not affect the PSD. Therefore, the correct option is (C).
.The power spectral density (PSD) is the Fourier transform of the autocorrelation function:
.Using the scaling property of the Fourier transform, , where :
.Note that the time shift in the process does not affect the autocorrelation of a WSS process, and consequently, it does not affect the PSD. Therefore, the correct option is (C).
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