1
GATE ECE 2013
+2
-0.6
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below.

The optimum threshold to achieve minimum bit error rate (BER) is

A
$${1 \over 2}$$
B
$${4 \over 5}$$
C
1
D
$${3 \over 2}$$
2
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
$$\left( {4\,{\pi ^2}{f^2} - 1} \right)\,\exp \left( { - \pi f} \right)$$
3
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
4
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
$$\infty$$
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