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 2022
MCQ (Single Correct Answer)
+2
-0.67

Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)$$, where x(t) and y(t) are the input and output respectively. Its impulse response is

A
$$2{e^{ - {1 \over 4}t}}u(t)$$
B
$$2{e^{ - 4t}}u(t)$$
C
$$8{e^{ - {1 \over 4}t}}u(t)$$
D
$$8{e^{ - 4t}}u(t)$$
3
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Consider the system as shown below:

GATE EE 2022 Signals and Systems - Linear Time Invariant Systems Question 8 English

where y(t) = x(et). The system is

A
linear and causal.
B
linear and non-causal.
C
non-linear and causal.
D
non-linear and non-causal.
4
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+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.
GATE EE Subjects
EXAM MAP