1
GATE ECE 2016 Set 1
Numerical
+1
-0
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23Hz. The fundamental frequency (in Hz) of the output is _____________________.
2
GATE ECE 2014 Set 4
+1
-0.3
A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose frequency response is
$$H(f) = \left\{ {\matrix{ {{e^{ - j4\pi f}},} & {\left| f \right| \le \,{W \over 2}} \cr {0,} & {\left| f \right| > \,{W \over 2}} \cr } } \right.$$

The output of the system is

A
x(t + 4)
B
x(t - 4)
C
x(t + 2)
D
x(t - 2)
3
GATE ECE 2013
+1
-0.3
Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is
A
u (t)
B
tu (t)
C
$${{{t^2}} \over 2}(t)$$
D
$${e^{ - t}}u(t)$$
4
GATE ECE 2013
+1
-0.3
Let g(t) = $${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is
A
$${e^{ - \pi {f^2}}}\,$$
B
$${e^{ - \pi {f^2}/2}}\,$$
C
$${e^{ - \pi \left| f \right|}}$$
D
$${e^{ - 2\pi {f^2}}}$$
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