1. What is the rule h*x = 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. 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.
3. 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. Does the system h(t) = exp(-7t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned
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
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
d) None of the mentioned
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
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
d) None of the mentioned
Explanation: The anti causal u[-n] term makes the system non causal.
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. Is y[n] = nu[n] a linear system?
a) Yes
b) No
Explanation: The system is linear s it obeys both homogeneity and the additive rules.