This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of LTI System in Z Domain”.

1. 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(π3n+5.2o)]u(n)**b) [1.099+1.088(0.9) ^{n}.cos(π3n−5.2o)]u(n)**

c) [1.099+1.088(0.9)

^{n}.cos(π3n−5.2o)]

d) None of the mentioned

2. 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**

3. 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

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. 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

6. 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)^{n}u(n)

b) 0.5(6.3)^{n}u(n)

c) 6.3(0.5)^{n}**d) 6.3(0.5) ^{n}u(n)**

7. 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

8. 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

9. 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

10. 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

11. A linear time invariant system is characterized by the system function H(z)=11−0.5z−1+21−3z−1. What is the h(n) if the system is stable?

a) (0.5)^{n}u(n)-2(3)^{n}u(n)

b) (0.5)^{n}u(-n-1)-2(3)^{n}u(-n-1)

c) (0.5)^{n}u(-n-1)-2(3)^{n}u(n)**d) (0.5) ^{n}u(n)-2(3)^{n}u(-n-1)**

12. A linear time invariant system is characterized by the system function H(z)=11−0.5z−1+21−3z−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

3.

13. A linear time invariant system is characterized by the system function H(z)=11−0.5z−1+21−3z−1. What is the h(n) if the system is anti causal?

a) (0.5)^{n}u(n)+2(3)^{n}u(n)

b) (0.5)^{n}u(-n-1)-2(3)^{n}u(-n-1)**c) -[(0.5) ^{n}+2(3)^{n}]u(-n-1)**

d) (0.5)

^{n}u(n)-2(3)

^{n}u(-n-1)