1
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________.

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2
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
$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = {\alpha _3}$$
3
GATE ECE 2015 Set 3
Numerical
+2
-0
Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limits_{n = - \infty }^\infty {\delta (t - 10n)} $$ Where ' * ' denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in samples/sec) for x(t) is __________________.
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4
GATE ECE 2015 Set 3
Numerical
+1
-0
Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area under g(t) is_______________.
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