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
+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
+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
+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
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
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