1
GATE ECE 2016 Set 3
+1
-0.3
Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t} \right),$$ where $$\,t$$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $$y\left( t \right)\, = x\,\,\left( {2t + 5} \right)$$ is
A
8
B
12
C
16
D
32
2
GATE ECE 2016 Set 1
+1
-0.3
A continuous -time function $$x\left( t \right)$$ is periodic with period $$T$$. The function is sampled uniformly with a sampling period $${T_s}$$. In which one of the following cases is the sampled signal periodic?
A
$$T\,\, = \,\,\sqrt 2 \,\,{T_s}$$
B
$$T\,\, = \,\,1.2T$$
C
Always
D
Never
3
GATE ECE 2015 Set 2
+1
-0.3
The signal $$\cos \left( {10\pi t + {\pi \over 4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $$\,\left( {{{\sin \left( {\pi t} \right)} \over {\pi t}}} \right)\,\cos \left( {40\pi t - {\pi \over 2}} \right).$$ The filter output is
A
$${{15} \over 2}\cos \left( {40\pi t - {\pi \over 4}} \right)$$
B
$${{15} \over 2}\left( {{{\sin \left( {\pi t} \right)} \over {\pi t}}} \right)\cos \left( {10\pi t + {\pi \over 4}} \right)$$
C
$${{15} \over 2}\cos \left( {10\pi t - {\pi \over 4}} \right)$$
D
$${{15} \over 2}\left( {{{\sin \left( {\pi t} \right)} \over {\pi t}}} \right)\cos \left( {40\pi t - {\pi \over 2}} \right)$$
4
GATE ECE 2014 Set 3
Numerical
+1
-0
A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$ where the baseband signal $$m\left( t \right)\,$$ has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which $$y\,\,\left( t \right)$$ should be sampled to recover $$m\,\,\left( t \right)$$ is ________.