This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of LTI Systems – II”.

1. What is the rule h*x = x*h called?

a) Commutativity rule

b) Associativity rule

c) Distributive rule

d) Transitive rule

View Answer

Explanation: By definition, the commutative rule h*x=x*h.

2. For an LTI discrete system to be stable, the square sum of the impulse response should be

a) Integral multiple of 2pi

b) Infinity

c) Finite

d) Zero

View Answer

Explanation: If the square sum is infinite, the system is an unstable system. If it is zero, it means h(t) = 0 for all t. However, this cannot be possible. Thus, it has to be finite.

3. What is the rule (h*x)*c = h*(x*c) called?

a) Commutativity rule

b) Associativity rule

c) Distributive rule

d) Transitive rule

View Answer

Explanation: By definition, the associativity rule = h*(x*c) = (h*x)*c.

a) Yes

b) No

c) Marginally Stable

View Answer

Explanation: The system corresponds to a stable system, as the Re(exp) term is negative, and hence will die down as t tends to infinity.

5. What is the following expression equal to: h*(d+bd), d(t) is the delta function

a) h + d

b) b + d

c) d

d) h + b

View Answer

Explanation: Apply commutative and associative rules and the convolution formula for a delta function

6. Does the system h(t) = exp([14j]t) correspond to a stable system?

a) Yes

b) No

c) Marginally Stable

View Answer

Explanation: The system corresponds to an oscillatory system, this resolving to a marginally stable system.

7. What is the rule c*(x*h) = (x*h)*c called?

a) Commutativity rule

b) Associativity rule

c) Distributive rule

d) Associativity and Commutativity rule

View Answer

Explanation: By definition, the commutative rule i h*x=x*h and associativity rule = h*(x*c) = (h*x)*c.

8. Is y[n] = n*sin(n*pi/4)u[-n] a causal system?

a) Yes

b) No

c) Marginally causal

View Answer

Explanation: The anti causal u[-n] term makes the system non causal.

a) True

b) False

View Answer

Explanation: By definition, the commutative rule i h*x=x*h=y. Thus, the response will be the same.

10. Is y[n] = nu[n] a linear system?

a) Yes

b) No

View Answer

Explanation: The system is linear s it obeys both homogeneity and the additive rules.

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