1
GATE ECE 2024
MCQ (More than One 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

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

2
GATE ECE 2024
MCQ (More than One Correct Answer)
+2
-0

The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are __.

A

0.15$\pi$

B

0.225$\pi$

C

0.3$\pi$

D

0.45$\pi$

3
GATE ECE 2024
Numerical
+2
-0

The relationship between any N-length sequence $x[n]$ and its corresponding N-point discrete Fourier transform $X[k]$ is defined as

$X[k] = \mathcal{F}\{x[n]\}$.

Another sequence $y[n]$ is formed as below

$y[n] = \mathcal{F}\{ \mathcal{F}\{ \mathcal{F}\{ \mathcal{F}\{x[n]\}\}\}\}\}$.

For the sequence $x[n] = \{1, 2, 1, 3\}$, the value of $Y[0]$ is _________.

Your input ____
4
GATE ECE 2024
MCQ (Single Correct Answer)
+1
-0.33

If ‘→’ denotes increasing order of intensity, then the meaning of the words [charm → enamor → bewitch] is analogous to [bored → _______ → weary]. Which one of the given options is appropriate to fill the blank?

A

jaded

B

baffled

C

dead

D

worsted

EXAM MAP