1
GATE ECE 2006
MCQ (Single Correct Answer)
+2
-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

A
$$2 \times {10^3}$$
B
$$4 \times {10^3}$$
C
$$6 \times {10^3}$$
D
$$8 \times {10^3}$$
2
GATE ECE 2006
MCQ (Single Correct Answer)
+2
-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
A
$${\delta (t)}$$
B
m(t)
C
0
D
m(t) $${\delta (t)}$$
3
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
A 1 kHz sinusoidal signal is ideally sampled at 1500 samples /sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency
A
zero Hz
B
0.75 kHz
C
0.5 kHz
D
0.25 kHz
4
GATE ECE 2003
MCQ (Single Correct Answer)
+2
-0.6
Let x(t) = $$\,2\cos (800\pi t) + \cos (1400\pi t)$$. x(t) is sampled with the rectangular pulse train shown in figure. The only spectral components (in KHz) present in the sampled signal in the frequency range 2.5 kHz to 3.5 kHz are
A
2.7, 3.4
B
3.3, 3.6
C
2.6, 2.7, 3.3, 3.4
D
2.7, 3.3
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