Signals & Systems Questions and Answers – Properties of LTI Systems – 3

This set of Signals & Systems online quiz focuses on “Properties of LTI Systems – 3”.

1. Which is special the property listed below only holds good by an LTI system?
a) Memory
b) Stability
c) Causality
d) Distributive property
View Answer

Answer: d
Explanation: An LTI system holds a unique property of Associativity, Commutativity and Distributive Property which are not held by other systems. They have very special representations in terms of convolution and integrals.

2. What are the three special properties that only LTI systems follow?
a) Commutative property, Associative property, Causality
b) Associative property, Distributive property, Causality
c) Commutative property, Distributive property, Associative property
d) Distributive property, Stability, Causality
View Answer

Answer: c
Explanation: Commutative property, Distributive property, Associative property are the unique properties of LTI systems which are special representations in terms of convolution and integrals.

3. Which is the commutative property of the LTI System in case of discrete time system?
a) x[n]+h[n]=h[n]+x[n]
b) x[n]+h[n]=h[n]*x[n]
c) x[n]*h[n]=h[n]*x[n]
d) x[t]*h[t]=h[n]*x[n]
View Answer

Answer: c
Explanation: We represent commutative property as: x[t]*h[t]=h[t]*x[t] because it proves that convolution of two signals in either order will be same, with x[n] being the input and h[n] being the impulse response.
advertisement
advertisement

4. Does the commutative property holds good for both continuous and discrete signal?
a) Yes
b) No
View Answer

Answer: a
Explanation: Yes, the commutative property is followed by both continuous time and discrete time LTI system. In this system, convolution of one side of the equation is equal to the other side.

5. Which is the correct representation of Commutative Continuous time LTI system?
a) ∫h(α) + x(t-α) = ∫x(α) + h(t-α)
b) ∫h(α)x(t-α) = ∫x(α)h(t-α)
c) ∫h(α) – x(t-α) = ∫x(α)h(t-α)
d) ∫h(α) * x(t-α) = ∫x(α) * h(t-α)
View Answer

Answer: b
Explanation: According to the commutative rule, x(t)*h(t) = h(t)*x(t)= ∫h(α)x(t-α) = ∫x(α)h(t-α), with x(t) being the input and h(t) being the impulse response.
Note: Join free Sanfoundry classes at Telegram or Youtube

6. What is the Distributive property of the LTI system?
a) x[n] + h1[n] + h2[n] = h1[n] + h2[n] + x[n]
b) x[n]*(h1[n] + h2[n]) = x[n]*(h1[n])*(x[n]*h2[n])
c) x[n]*(h1[n] + h2[n]) = x[n]*h1[n] + x[n]*h2[n]
d) x[n]*(h1[n] + h2[n]) = *(x[n]*h1[n]) + x[n]*h2[n]
View Answer

Answer: c
Explanation: x[n]*(h1[n] + h2[n]) = x[n]*h1[n] + x[n]*h2[n], with x[n] being the input and h1[n] and h2[n] being the impulse responses.

7. What does the Distributive property signify?
a) The sum of signals in both the sides in any number must be equal
b) The responses must be equal in any side of an LTI system
c) The sum of two inputs must be equal to responses to these signals
d) The Multiplication of two signals in the inputs side is equal to multiplication of the responses
View Answer

Answer: c
Explanation: The sum of two inputs must be equal to responses to these signals individually.
x[n]*(h1[n]+h2[n])=x[n]*h1[n]+x[n]*h2[n], with x[n] being the input and h1[n] and h2[2] being the impulse responses.
advertisement

8. Which is the associative property of the LTI system?
a) x[n]*(h1[n]+h2[n])=x[n]*h1[n]+x[n]*h2[n]
b) x[n]*(h1[n]*h2[n])=h1[n]+x[n]+h2[n]
c) x[n]*h[n]=h[n]*x[n]
d) x[n]*(h1[n]*h2[n])=(x[n]*h1[n])*h2[n]
View Answer

Answer: d
Explanation: x[n]*(h1[n]*h2[n])=(x[n]*h1[n])*h2[n], with x[n] being the input and h1[n] and h2[n] being the impulse responses which is the associative property.

9. What does the associative property apply?
a) Parallel connection of two systems is equivalent to a single system only in case of a continuous system
b) Series and parallel interconnection of two systems is equivalent to a single system only in case of discrete system
c) Series interconnection of two systems is equivalent to a single system in case of both continuous and discrete system
d) Series interconnection of two systems is equivalent to a single system only in case of discrete
View Answer

Answer: c
Explanation: Series interconnection of two systems is equivalent to a single system in case of both continuous and discrete system. This can be generalized to an arbitrary number of LTI systems in cascade.
advertisement

10. The order of the Cascade system doesn’t depend on the output. Which is the property?
a) Commutative
b) Associative
c) Commutative and distributive
d) Distributive
View Answer

Answer: b
Explanation: Series interconnection of two systems is equivalent to a single system in case of both continuous and discrete system, which is the associative property. This can be generalized to an arbitrary number of LTI systems in cascade.

Sanfoundry Global Education & Learning Series – Signals & Systems.

To practice all areas of Signals & Systems for online Quizzes, here is complete set of 1000+ Multiple Choice Questions and Answers.

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses.