1
GATE ECE 2011
+2
-0.6
X(t) is a stationary random process with autocorrelation function Rx$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ^2}} \right)$$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is
A
$$\left( {4\,{\pi ^2}{f^2} + 1} \right)\,\exp \left( { - \pi {f^2}} \right)$$
B
$$\left( {4\,{\pi ^2}{f^2} - 1} \right)\,\exp \left( { - \pi {f^2}} \right)$$
C
$$\left( {4\,{\pi ^2}{f^2} + 1} \right)\,\exp \left( { - \pi f} \right)$$
D
$$\left( {4\,{\pi ^2}{f^2} - 1} \right)\,\exp \left( { - \pi f} \right)$$
2
GATE ECE 2010
+2
-0.6
X(t) is a stationary process with the power spectral density Sx(f) > 0 for all f. The process is passed through a system shown below.

Let Sy(f) be the power spectral density of Y(t). Which one of the following statements is correct?

A
Sy(f) > 0 for all f
B
Sy(f) > 0 for $$\left| f \right|$$ > 1 kH
C
Sy(f) > 0 for f = nf0, f0 = 2kHz, n any integer
D
Sy(f) > 0 for f = (2n + 1)f0, f0 = 1 kHz, n any integer
3
GATE ECE 2008
+2
-0.6
Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of fc. The noise power at the filter output is
A
K
B
K fc
C
K $$\pi$$ fc
D
$$\infty$$
4
GATE ECE 2006
+2
-0.6
A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period ts = 0.03 msec. The samples so obtained would be
A
correlated
B
statistically independent
C
uncorrelated
D
orthogonal
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