1
GATE ECE 2026
MCQ (Single Correct Answer)
+1
-0.33

Two analog signals $x_1(t)$ and $x_2(t)$ ( $t$ in second), are sampled at a rate $F_s=40 \mathrm{~Hz}$, where $x_1(t)=\cos (20 \pi t), t \geq 0$, and $x_2(t)=\cos (100 \pi t), t \geq 0$.

The first ten samples (starting from $t=0$ ) are considered for the analysis.

Which of the following statements is TRUE?

A

All of the first three samples of $x_1(t)$ are greater than the corresponding samples of $x_2(t)$.

B

All of the last three samples of $x_1(t)$ are greater than the corresponding samples of $x_2(t)$.

C

All of the samples of $x_2(t)$ are greater than the corresponding samples of $x_1(t)$.

D

All of the fourth to seventh samples of $x_1(t)$ are equal to the corresponding samples of $x_2(t)$.

2
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+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 2016 Set 3
MCQ (Single Correct Answer)
+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
4
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+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
$${{15} \over 2}\left( {{{\sin \left( {\pi t} \right)} \over {\pi t}}} \right)\cos \left( {40\pi t - {\pi \over 2}} \right)$$

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