1
GATE EE 2024
+2
-1.33

The input $x(t)$ and the output $y(t)$ of a system are related as

$$y(t) = e^{-t} \int\limits_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad - \infty < t < \infty.$$

The system is

A

nonlinear.

B

linear and time-invariant.

C

linear but not time-invariant.

D

noncausal.

2
GATE EE 2024
+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.

3
GATE EE 2015 Set 2
+2
-0.6
For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?
A
The impulse response will be integral, but may not be absolutely integrable.
B
The unit impulse response will have finite support.
C
The unit step response will be absolutely integrable.
D
The unit step response will be bounded.
4
GATE EE 2013
+2
-0.6
The impulse response of a continuous time system is given by h(t) = $$\delta$$(t − 1) + $$\delta$$(t − 3). The value of the step response at t = 2 is
A
0
B
1
C
2
D
3
EXAM MAP
Medical
NEET