# Signals & Systems Questions and Answers – Properties of LTI Systems – 1

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of LTI Systems – 1”.

1. What is the rule h*(x+y) = (y+x)*h called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

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

2. Does the system h(t) = exp([-1-2j]t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

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

3. What is the rule h*(x*c) = (x*h)*c called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Associativity and Commutativity rule

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

4. Is y[n] = n*cos(n*pi/4)u[n] a stable system?
a) Yes
b) No
c) Marginally stable
d) None of the mentioned

Explanation: The ‘n’ term in the y[n] will dominate as it reaches to infinity, and hence could reach infinite values.

5. What is the rule (h*x)*c = h*(x*c) called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

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

4. Is y[n] = n*sin(n*pi/4)u[-n] a stable system?
a) Yes
b) No
c) Marginally stable
d) None of the mentioned

Explanation: The ‘n’ term in the y[n] will dominate as it reaches to negative infinity, and hence could reach infinite values. Eventhough + infinity would not be a problem, still the resultant system would be unstable.

7. What is the following expression equal to: h*(c*(b+d(t))), d(t) is the delta function
a) h*c + h*b
b) h*c*b + b
c) h*c*b + h*c
d) h*c*b + h

Explanation: Apply commutative and associative rules

8. Does the system h(t) = exp([1-4j]t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

Explanation: The system corresponds to an unstable system, as the Re(exp) term is a positive quantity.

9. The system transfer function and the input if exchanged will still give the same response.
a) True
b) False

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

10. 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

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.

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