GATE ECE 2006 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

The Dirac delta function $$\delta (t)$$ is defined as

$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\delta (t - 0.5x{{10}^{ - 4}}k)} $$
The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be

$${\delta (t)}$$

m(t)

m(t) $${\delta (t)}$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {{{\sin \,\,2\,\pi \,1000\,t)} \over {\pi \,t}}} \right)^3} + 7{\left( {{{\sin \,\,2\,\pi \,1000\,t} \over {\pi \,t}}} \right)^2}$$

would be

$$2 \times {10^3}$$

$$4 \times {10^3}$$

$$6 \times {10^3}$$

$$8 \times {10^3}$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if

$$A(\omega ) = C{\omega ^2},\,\,\phi (\omega ) = K{\omega ^3}$$

$$A(\omega ) = C{\omega ^2},\,\,\phi (\omega ) = K\omega $$

$$A(\omega ) = C\omega ,\,\,\phi (\omega ) = K{\omega ^2}$$

$$A(\omega ) = C,\,\,\phi (\omega ) = K{\omega ^{ - 1}}$$

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