1
GATE ECE 2014 Set 1
Numerical
+1
-0
Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and $$y\left( t \right)$$ band - limited to $$\,\left[ { - 1\,\,kHz,\,\,1kHz} \right].$$ For $$z\left( t \right)\,\, = \,x\left( t \right).y\left( t \right),$$ the Nyquist sampling frequency $$\left( {in\,\,kHz} \right)$$ is________.
2
GATE ECE 2013
MCQ (Single Correct Answer)
+1
-0.3
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is
A
5 kHz
B
12 kHz
C
15 kHz
D
20 kHz
3
GATE ECE 2002
MCQ (Single Correct Answer)
+1
-0.3
Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^{ + \infty } {\delta \left( {t - n{T_s}} \right)}$$

where $$x\left( t \right) = 10\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$ and
$${T_s} = 100\,\,\mu \sec .$$ When $$y\left( t \right)$$ is passed through an ideal low-pass filter with a cutoff frequency of 5 KHz, the output of the filter is

A
$$5 \times {10^{ - 6}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
B
$$5 \times {10^{ - 5}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
C
$$5 \times {10^{ - 1}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
D
$$10\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
4
GATE ECE 2001
MCQ (Single Correct Answer)
+1
-0.3
A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through
A
an RC filter
B
an envelope detector
C
a PLL
D
an ideal low-pass filter with the appropriate bandwidth
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