When a discrete time LTI system is said to be causal? must not depend on x for k>n b) Output y must not depend on x for k=n c) Output y must not depend on x for k<n d) Output y must depend on x for k>n

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

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

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

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)

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 the following statements for continuous-time linear time invariant (LTI) systems.
1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. 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 1 and 2 are true

B

Both 1 and 2 are not true

C

Only 1 is true

D

Only 2 is true

If H(z) is the system function of an LTI system and HI(z) is the system function of the inverse LTI system, then which of the following is true?

A

H(z)*HI(z)=1

B

H(z)*HI(z)=δ(n)

C

H(z).HI(z)=1

D

H(z).HI(z)=δ(n)

Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

A

$${1 \over 5}{e^{3t}}u\left( { - t} \right) + {1 \over 5}{e^{ - 2t}}u\left( { - t} \right)$$

B

$$ - {1 \over 5}{e^{3t}}u\left( { - t} \right) + {1 \over 5}{e^{ - 2t}}u\left( { - t} \right)$$

C

$${1 \over 5}{e^{3t}}u\left( { - t} \right) - {1 \over 5}{e^{ - 2t}}u\left( t \right)$$

D

$$ - {1 \over 5}{e^{3t}}u\left( { - t} \right) - {1 \over 5}{e^{ - 2t}}u\left( t \right)$$

The process of converting discrete-time continuous valued signal into discrete-time discrete valued (digital) signal is known as ____________

A

Sampling

B

Quantization

C

Coding

D

None of the mentioned

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

When a discrete time LTI system is said to be causal? must not depend on x for k>n b) Output y must not depend on x for k=n c) Output y must not depend on x for kn

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