1
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

Consider the discrete-time systems $T_1$ and $T_2$ defined as follows:

{ $T_1 x[ n ] = x[ 0 ] + x[ 1 ] + \cdots + x[ n ] $}

{ $T_2 x[ n ] = x[ 0 ] + \frac{1}{2} x[ 1 ] + \cdots + \frac{1}{2^n} x[ n ] $}

Which one of the following statements is true?

A

$T_1$ and $T_2$ are BIBO stable.

B

$T_1$ and $T_2$ are not BIBO stable.

C

$T_1$ is BIBO stable but $T_2$ is not BIBO stable.

D

$T_1$ is not BIBO stable but $T_2$ is BIBO stable.

2
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n] = x[2n]$ is

A

$Y(z) = X(z^2)$

B

$Y(z) = \frac{1}{2} \left[ X(z^{-1/2}) + X(-z^{-1/2}) \right]$

C

$Y(z) = \frac{1}{2} \left[ X(z^{1/2}) + X(-z^{1/2}) \right]$

D

$Y(z) = \frac{1}{2} \left[ X(z^2) + X(-z^2) \right]$

3
GATE EE 2024
Numerical
+2
-1.33

If the energy of a continuous-time signal $x(t)$ is $E$ and the energy of the signal $2x(2t - 1)$ is $cE$, then $c$ is _____ (rounded off to 1 decimal place).

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

If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → _______ → pander].
Which one of the given options is appropriate to fill the blank?

A

flatter

B

flutter

C

fritter

D

frizzle

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