1
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
$$\infty$$
2
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
3
GATE ECE 2006
+2
-0.6
The following question refer to wide sense stationary stochastic process:

It is desired to generate a stochastic process (as voltage process) with power spectral density

$$S\left( \omega \right) = {{16} \over {16 + {\omega ^2}}}$$\$

By driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with power spectral density being constant equal to 1. The system which can perform the desired task could be

A
first order lowpass R-L filter
B
first order highpass R-c filter
C
tuned L-C filter
D
series R-L-C filter
4
GATE ECE 2006
+2
-0.6
The following question refer to wide sense stationary stochastic process:

The parameters of the system obtained in Q. 12 would be

A
first order R-L low pass filter would have $$R = 4\Omega \,L = 1\,H$$
B
first order R-C high pass filter would have $$R = 4\Omega \,C = 0.25F$$
C
tuned L-C filter would have $$L = 4H\,\,C = 4F.$$
D
series R-L-C low pass filter would have $$R = 1\Omega ,\,L = 4H,\,\,C = 4F.$$
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