1
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
$${\alpha _1} = {\alpha _2} = 0;\,{\alpha _0} = {\alpha _3}$$
2
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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3
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_______________.
Your input ____
4
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The complex envelope of the bandpass signal $$x(t) = - \sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,\sin \,\left( {\pi t - {\pi \over 5}} \right)$$, 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
$$\sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,{e^{-j{\pi \over 4}}}$$
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