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

a) Memory

b) Stability

c) Causality

d) Distributive property

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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

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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]

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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.

4. Does the commutative property holds good for both continuous and discrete signal?

a) Yes

b) No

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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.

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)

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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.

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]

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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

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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.

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]

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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.

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

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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.

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

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.

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