# Signals & Systems Questions and Answers – Properties of LTI Systems – 4

This set of Signals & Systems Question Bank focuses on “Properties of LTI Systems – 4”.

1. What are the properties of an LTI system posse other than Associative, Commutative and Distributive properties?
a) Memory, invertibility, causality, stability
b) Memory and non-causality
c) Invertibility and stability
d) Causality only

Explanation: A LTI System follows most of the properties that a normal system follows. This includes memory and memory-less property, invertibility, causality and stability.

2. An LTI system is memoryless only if ____________
a) It does not store the previous value of the input
b) It does not depend on any previous value of the input
c) It does not depend on stored values of the system
d) It does not depend on the present value of the input

Explanation: A LTI system is said to be memoryless only if it does not depend on any previous value of the input. That is we can say that if its output at any time depends only on the value of the input at the same time.

3. A continuous time LTI system has memory only when __________
a) It does not depend on the present value of the input
b) It only depends on the past values of the input
c) Its output always depends both on the previous and past values of the input
d) Its output might depend on the present value as well as the previous value of the input

Explanation: An LTI system is said to have a memory when its output at any time depends on the previous value of the input. This does not mean its value does not depend on present values. It depends both on past and present values according to the situation.

4. Which of the following system is memoryless?
a) h(t)=0,t ≠0
b) h(t)=x(t-1)
c) h(t)=0, t=0
d) h(t)=kx(t+2)

Explanation: A continuous-time LTI system is memoryless when h(t)=0,t ≠0. Such memoryless system has the form h(t)=kx(t), for some constant k has the impulse response h(t) = k∂(t).

5. A continuous time LTI system is invertible only when its inverse exists.
a) True
b) False

Explanation: Yes, a continuous time LTI system is invertible only when its inverse exists that, when connected in series with the original system produces an output equal to the input to the first system. Furthermore, if a system is invertible we can say its inverse exists.
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6. Invertibility is only followed by continuous time LTI systems.
a) True
b) False

Explanation: False, discrete time LTI System also follows invertibility properties. It can be shown by Impulse response h1[n] of the inverse system for an LTI system for an impulse response h[n] must satisfy
h[n]*h1[n]=∂[n].

7. Which property of an LTI system does the following equation prove h[n]*h1[n]=∂[n]?
a) Invertibility
b) Stability
c) Associativilty
d) Commutative

Explanation: This equation proves that the condition that h1[n] must satisfy to be the impulse response of the inverse system in case of discrete time LTI system. Thus this gives the necessary condition for the invertibility property of an LTI system.

8. A continuous time LTI system is causal only when __________
a) It depends on the present value of the input
b) It depends on the past values of the input
c) Its output always depends on future values of the input
d) Its output might depend only on the past and present values of the system

Explanation: An LTI system is said to be causal when its output at any time depends on the previous and present value of the input. That is its value does not depend only on past values.

9. An important property for causality of the system is __________
a) Initial rest
b) Final rest
c) It is memoryless
d) It is unstable

Explanation: A causal system follows what is called initial rest concept. That is if the input of the system is 0 upto some point in time than the output of the system should also be zero upto that time.

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

Explanation: A causal system cannot depend on the future values of the input. It can only depend on the past values or present values.

11. Which of the following system is causal?
a) y[n] = 2[n] – 3[n+1]
b) y[n] = 2[n] + 3
c) y[n] = 2[n-7] – 3[n+1]
d) y[n] = 2[n]*3[n+1]

Explanation: An LTI system is said to be causal only when its output at any time depends on the previous or present value of the input. A causal system cannot depend on the future values of the input.

12. When are LTI systems stable?
a) Only when bounded input produces a bounded output
b) Only when bounded input produces a unbounded output
c) Only when unbounded input produces a bounded output
d) Only when unbounded input produces an unbounded output

Explanation: It follows from previous BIBO stability factor. It is the same for an LTI system too. Hence, a continuous or discrete time LTI system is said to be stable only when bounded input produces a bounded output.

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