Consider the following statements for continuous-time linear time invariant (LTI) systems.<br>1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.<br>2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.<br>Which one among the following is correct?

Consider the following statements for continuous-time linear time invariant (LTI) systems. I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. II. There is no causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?

A

Both I and II are true

B

Both I and II are not true

C

Only I is true

D

Only II is true

Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image

Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.

A

Causal, LP

B

BIBO, LTI

C

BIBO, Causal, LTI

D

LP, LTI

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S₂ : The system is stable but not causal for
$$ROC:\left| z \right| S₃ : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?

A

Both S₁ and S₂ are true

B

Both S₂ and S₃ true

C

Both S₁ and S₃ are true

D

S₁, S₂ and S₃ are all true

Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P₁, P₂ and P₃ with system relations R₁, R₂, P₃, P₄.
Properties
P₁ : Linear but NOT time-invariant
P₂ : Time-invariant but NOT linear
P₃ : Linear and time-invariant
Relations
R₁ : y(t) = t²x(t)
R₂ : y(t) = t |x(t)|
R₃ : y(t) = |x(t)|
R₄ : y(t) = x(t - 5)

A

(P₁, R₁), (P₂, R₃), (P₃, R₄)

B

(P₁, R₂), (P₂, P₃), (P₃, R₄)

C

(P₁, R₃), (P₂, R₁), (P₃, R₂)

D

(P₁, R₁), (P₂, R₂), (P₃, R₃)

A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$ To make this system causal it needs to be cascaded with another LTI system having a transfer function H₁(s). A correct choice for H₁(s) among the following options is

A

s + 3

B

s - 2

C

s - 6

D

s + 1

Which of the following statements are correct? 1. A continuous-time system is said to be time-invariant if the parameters of the system do not change with time. 2. The characteristics of a time-invariant system are fixed over time. 3. If the input to the time-invariant system is delayed by t0 seconds, the characteristics of the output response are also delayed by t0 seconds.

A

1 and 2 only

B

1 and 3 only

C

2 and 3 only

D

1, 2 and 3

The input x[n] and output y[n] of a discrete-time system are related as y[n] = αy [n - 1] + x[n]. The condition on α for which the system is Bounded-Input Bounded-Output (BIBO) stable is

A

|α| < 1

B

|α| = 1

C

|α| > 1

D

|α| < 3/2

A system provides output yi(t) when xi(t) is applied. If the system is said to be LTI then which of the following properties must satisfy? (i).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) + by2(t) (ii).If the input is x(t – T), then the output must be y (t – T) (iii).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) * by2(t) (iv).If the input is x(t – T), then the output must be y(t + T)

A

(i), (ii) and (iv)

B

(i), (ii) and (iii)

C

(ii), (iii) and (iv)

D

(i) and (ii)

The impulse response functions of four linear systems S₁, S₂, S₃, S₄ are given respectively by
$${h_1}\left( t \right) = 1,$$ $${h_2}\left( t \right) = u\left( t \right),$$ $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$ $${h_4}\left( t \right) = {e^{ - 3t}}u\left( t \right)$$
Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?

A

S₁

B

S₂

C

S₃

D

S₄

Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$ Consider the following three statements:
S₁ : The system is stable.
S₂ : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$ independent of t for t > 0.
S₃ : A non-causal system with the same transfer function is stable.
For the above system,

A

Only S₁ and S₂ are true

B

Only S₂ and S₃ are true

C

Only S₁ and S₃ are true

D

S₁, S₂ and S₃ are true

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