## 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

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

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

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

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(Ï€n/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)

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(Ï€n/4)u(n) and the system is initially at rest?
a) 13.56cos(Ï€n/4 -28.7o)
b) 13.56cos(Ï€n/4 +28.7o)u(n)
c) 13.56cos(Ï€n/4 -28.7o)u(n)
d) None of the mentioned

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

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)

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)

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

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(Ï€/3n+5.2o)]u(n)
b) [1.099+1.088(0.9)n.cos(Ï€/3n−5.2o)]u(n)
c) [1.099+1.088(0.9)n.cos(Ï€/3n−5.2o)]
d) None of the mentioned

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