1
GATE ECE 2010
+2
-0.6
Consider a base band binary PAM receiver shown below. The additive channel noise $$n(t)$$ is white with power spectral density $${S_N}\left( f \right) = {N_0}/2 = {10^{ - 20}}$$ $$W/Hz$$. The low-pass filter is ideal with unity gain and cut -off frequency $$1MHz$$. Let $${Y_k}$$ represent the random variable $$y\left( {{t_k}} \right)$$.
$${Y_k} = {N_k}$$ if transmitted bit $${b_k} = 0$$
$${Y_k} = a + {N_k}$$ if transmitted bit $${b_k} = 1$$
Where $${b_k} = 0$$ represents the noise sample value. The noise sample has a probability density function, $${P_{{N_k}}}\left( n \right)\,\,\,\,\,\,\, = 0.5\alpha {e^{ - \alpha \left| n \right|}}$$ (This has mean zero and variance $$2/{\alpha ^2}$$). Assume transmitted bits to be equiprobable and threshold $$z$$ is set to $$a/2 = {10^{ - 6}}V$$.

The value of the parameter $$\alpha$$( in V-1 ) is

A
$${10^{10}}$$
B
$${10^{7}}$$
C
$$1.414 \times {10^{ - 10}}$$
D
$$2 \times {10^{ - 20}}$$
2
GATE ECE 2010
+2
-0.6
Consider a base band binary PAM receiver shown below. The additive channel noise $$n(t)$$ is white with power spectral density $${S_N}\left( f \right) = {N_0}/2 = {10^{ - 20}}$$ $$W/Hz$$. The low-pass filter is ideal with unity gain and cut -off frequency $$1MHz$$. Let $${Y_k}$$ represent the random variable $$y\left( {{t_k}} \right)$$.
$${Y_k} = {N_k}$$ if transmitted bit $${b_k} = 0$$
$${Y_k} = a + {N_k}$$ if transmitted bit $${b_k} = 1$$
Where $${b_k} = 0$$ represents the noise sample value. The noise sample has a probability density function, $${P_{{N_k}}}\left( n \right)\,\,\,\,\,\,\, = 0.5\alpha {e^{ - \alpha \left| n \right|}}$$ (This has mean zero and variance $$2/{\alpha ^2}$$). Assume transmitted bits to be equiprobable and threshold $$z$$ is set to $$a/2 = {10^{ - 6}}V$$.

The probability of bit error is

A
$$0.5 \times {e^{ - 3.5}}$$
B
$$0.5 \times {e^{ - 5}}$$
C
$$0.5 \times {e^{ - 7}}$$
D
$$0.5 \times {e^{ - 10}}$$
3
GATE ECE 2010
+1
-0.3
The transfer function Y(s)/R(s) of the system shown is
A
$$0$$
B
$$\frac1{s+1}$$
C
$$\frac1{s+2}$$
D
$$\frac2{s+3}$$
4
GATE ECE 2010
+1
-0.3
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output y(t)=$$\cos \left( {2t - {\pi \over 3}} \right),$$ for input signal x(t)=$$p\cos \left( {2t - {\pi \over 2}} \right).$$ Then the system parameter 'p' is
A
$$\sqrt 3$$
B
$${2 \over {\sqrt 3 }}$$
C
1
D
$${{\sqrt 3 } \over 2}$$
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