1
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
The impulse response of an LTI system can be obtained by
A
differentiating the unit ramp response
B
differentiating the unit step response
C
integrating the unit ramp response
D
integrating the unit step response
2
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\sin \left( {\pi t - {\pi \over 4}} \right),$$ centered about f = $${1 \over {2\,}}\,Hz,$$ is
A
$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$
B
$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$
C
$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$
D
$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$
3
GATE ECE 2015 Set 3
Numerical
+2
-0
Two sequence $${x_1}\left[ n \right]$$ and $${x_2}\left[ n \right]$$ have the same energy.
Suppose $${x_1}\left[ n \right]$$ $$ = \alpha \,{0.5^n}\,u\left[ n \right],$$ where $$\alpha $$ is a positive real number and $$u\left[ n \right]\,$$ is the unit step sequence. Assume $$${x_2}\left[ n \right] = \,\left\{ {\matrix{ {\sqrt {1.5} } & {for\,\,\,n = 0,1} \cr 0 & {otherwise} \cr } } \right.$$$

Then the value of $$\,\alpha $$ is________.

Your input ____
4
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider a four-point moving average filter defined by the equation $$y[n] = \sum\limits_{i = 0}^3 {{\alpha _i}x[n - i]} $$. The condition on the filter coefficients that results in a null at zero frequency is
A
$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = - {\alpha _3}$$
B
$${\alpha _1} = {\alpha _2} = 1;\,{\alpha _0} = - {\alpha _3}$$
C
$${\alpha _0} = {\alpha _3} = 0;\,{\alpha _1} = {\alpha _2}$$
D
$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = {\alpha _3}$$
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