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GATE EC 2019 Set 1 — Question 55

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NAT+2 / -0MediumFiltering Through LTI SystemsRandom ProcessesCommunicationsAutocorrelation & PSD

Communications → Random Processes → Autocorrelation & PSD

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Question

Let a random process Y(t)Y(t) be described as Y(t)=h(t)∗X(t)+Z(t)Y(t) = h(t) * X(t) + Z(t), where X(t)X(t) is a white noise process with power spectral density SX(f)=5S_X(f) = 5 W/Hz. The filter h(t)h(t) has a magnitude response given by ∣H(f)∣=0.5|H(f)| = 0.5 for −5≤f≤5-5 \le f \le 5, and zero elsewhere. Z(t)Z(t) is a stationary random process, uncorrelated with X(t)X(t), with power spectral density as shown in the figure. The power in Y(t)Y(t), in watts, is equal to ________ W (rounded off to two decimal places).
Power spectral density $S_Z(f)$ of random process $Z(t)$ showing a triangular shape from $f = -5$ to $f = 5$ with a peak value of 1 at $f = 0$.
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