Analysis of LTI System in Z Domain Multiple Choice Questions

 Analysis of LTI System in Z Domain

1. If one or more poles are located near the unit circle, then the rate of decay of signal is _________
a) Slow
b) Constant
c) Rapid
d) None of the mentioned
Answer: Slow

2. If p_k, k=1,2,…N are the poles of the system and |p_k| < 1 for all k, then the natural response of such a system is called as Transient response.
a) True
b) False
Answer: True

3. If all the poles of H(z) are outside the unit circle, then the system is said to be ________

a) Only causal
b) Only BIBO stable
c) BIBO stable and causal
d) None of the mentioned
Answer: None of the mentioned

4. If all the poles have small magnitudes, then the rate of decay of signal is __________
a) Slow
b) Constant
c) Rapid
d) None of the mentioned
Answer: Rapid

5. What is the transient response of the system described by the difference equation y(n)=0.5y(n-1)+x(n) when the input signal is x(n)= 10cos(πn/4)u(n) and the system is initially at rest?
a) (0.5)ⁿu(n)
b) 0.5(6.3)ⁿu(n)
c) 6.3(0.5)ⁿ
d) 6.3(0.5)ⁿu(n)
Answer: 6.3(0.5)ⁿu(n)

6. What is the steady-state response of the system described by the difference equation y(n)=0.5y(n-1)+x(n) when the input signal is x(n)= 10cos(πn/4)u(n) and the system is initially at rest?
a) 13.56cos(πn/4 -28.7^o)
b) 13.56cos(πn/4 +28.7^o)u(n)
c) 13.56cos(πn/4 -28.7^o)u(n)
d) None of the mentioned
Answer: 13.56cos(πn/4 -28.7^o)u(n)

7. If all the poles of H(z) are inside the unit circle, then the system is said to be ________
a) Only causal
b) Only BIBO stable
c) BIBO stable and causal
d) None of the mentioned
Answer: BIBO stable and causal

8. A linear time invariant system is characterized by the system function H(z)=(1/1−0.5z^-1)+(2/1−3z^-1). What is the h(n) if the system is stable?
a) (0.5)ⁿu(n)-2(3)ⁿu(n)
b) (0.5)ⁿu(-n-1)-2(3)ⁿu(-n-1)
c) (0.5)ⁿu(-n-1)-2(3)ⁿu(n)
d) (0.5)ⁿu(n)-2(3)ⁿu(-n-1)
Answer: (0.5)ⁿu(n)-2(3)ⁿu(-n-1)

9. A linear time invariant system is characterized by the system function H(z)=(1/1−0.5z^-1)+(2/1−3z^-1). What is the h(n) if the system is anti causal?
a) (0.5)ⁿu(n)+2(3)ⁿu(n)
b) (0.5)ⁿu(-n-1)-2(3)ⁿu(-n-1)
c) -[(0.5)ⁿ+2(3)ⁿ]u(-n-1)
d) (0.5)ⁿu(n)-2(3)ⁿu(-n-1)
Answer: -[(0.5)ⁿ+2(3)ⁿ]u(-n-1)

10. A linear time invariant system is characterized by the system function H(z)=(1/1−0.5z^-1)+(2/1−3z^-1). What is the ROC of H(z) if the system is causal?
a) |z|<3
b) |z|>3
c) |z|<0.5
d) |z|>0.5
Answer: |z|>3

11. What is the unit step response of the system described by the difference equation?
y(n)=0.9y(n-1)-0.81y(n-2)+x(n) under the initial conditions y(-1)=y(-2)=0?
a) [1.099+1.088(0.9)ⁿ.cos(π/3n+5.2^o)]u(n)
b) [1.099+1.088(0.9)ⁿ.cos(π/3n−5.2^o)]u(n)
c) [1.099+1.088(0.9)ⁿ.cos(π/3n−5.2^o)]
d) None of the mentioned
Answer: [1.099+1.088(0.9)ⁿ.cos(π/3n−5.2^o)]u(n)

12. If the ROC of the system function is the exterior of a circle of radius r < ∞, including the point z = ∞, then the system is said to be ___________
a) Stable
b) Causal
c) Anti causal
d) None of the mentioned
Answer: Causal

13. A linear time invariant system is said to be BIBO stable if and only if the ROC of the system function _____________
a) Includes unit circle
b) Excludes unit circle
c) Is an unit circle
d) None of the mentioned
Answer: Includes unit circle