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 GATE ECE 2003 Signals and Systems - Sampling Question 10 English
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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