1
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $\left[-\omega_c, \omega_c\right]$, where $\omega_c$ is in rad/sec.

The signal $f(t)$ is uniformly sampled to obtain $y(t)=f(t) p(t)$. Here

$$ p(t)=\sum_{n=-\infty}^{\infty} \delta\left(t-\tau-n T_s\right) $$

with $\delta(t)$ being the Dirac impulse, $T_s>0$, and $\tau>0$. The sampled signal $y(t)$ is passed through an ideal lowpass filter $h(t)=\omega_c T_s \frac{\sin \left(\omega_c t\right)}{\pi \omega_c t}$ with cutoff frequency $\omega_c$ and passband gain $T_s$.

The output of the filter is given by $\qquad$ .

A
$f(t)$ if $T_s<\pi / \omega_c$
B
$f(t-\tau)$ if $T_s<\pi / \omega_c$
C
$f(t-\tau)$ if $T_s<2 \pi / \omega_c$
D
$T_s f(t)$ if $T_s<2 \pi / \omega_c$
2
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

A continuous time signal $x(t) = 2 \cos(8 \pi t + \frac{\pi}{3})$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response

$h(t) = \left( \frac{\sin 2 \pi t}{\pi t} \right) \cos(38 \pi t - \frac{\pi}{2})$

produces an output $x_o(t)$. The expression for $x_o(t)$ is ______.

A

$15 \sin(38 \pi t + \frac{\pi}{3})$

B

$15 \sin(38 \pi t - \frac{\pi}{3})$

C

$15 \cos(38 \pi t - \frac{\pi}{6})$

D

$15 \cos(38 \pi t + \frac{\pi}{6})$

3
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response H(f) as following: $$H(f) = \left\{ {\matrix{ {1,} & {\left| f \right| \le \,12\,kHz} \cr {0,} & {\left| f \right| > \,12\,kHz} \cr } } \right.$$

What is the number of sinusoids in the output and their frequency inkHz?

A
Number = 1, frequency = 7
B
Number =3, frequencies =2, 7, 11
C
Number =2, frequencies =2, 7
D
Number =2, frequencies =7, 11
4
GATE ECE 2015 Set 3
Numerical
+2
-0
Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limits_{n = - \infty }^\infty {\delta (t - 10n)} $$ Where ' * ' denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in samples/sec) for x(t) is __________________.
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