1
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
$${{15} \over 2}\left( {{{\sin \left( {\pi t} \right)} \over {\pi t}}} \right)\cos \left( {40\pi t - {\pi \over 2}} \right)$$
2
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 ________.
3
GATE ECE 2014 Set 3
+1
-0.3
Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \right)$$ be sampled at $$20\,\,\,Hz$$ and reconstructed using an ideal low-pass filter with cut-off frequency of $$20\,\,\,Hz$$. The frequency/frequencies present in the reconstructed signal is/are.
A
5 Hz and 15 Hz only
B
10 Hz and 15 Hz only
C
5 Hz, 10 Hz and 15 Hz only
D
5 Hz only
4
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________.