# The Inverse Z-transform and Response of Linear Discrete Systrems MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Inverse Z-transform and Response of Linear Discrete Systrems”.

1. Inverse z-transform of the system can be calculated using:
a) Partial fraction method
b) Long division method
c) Basic formula of the z-transform
d) All of the mentioned

2. Assertion (A): The system function
H(z) = z3-2z2+z/z2+1/4z+1/s is not causal
Reason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not correct Explanation of A
c) A is True and R is false
d) A is False and R is true

3. Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is:
a) z2/(z+1)(z-1)
b) z/(z+1)(z-1)
c) z+1/z-1
d) z(z-1)/z+1

4. Assertion (A): Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.
Reason(R): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not correct Explanation of A
c) A is True and R is false
d) A is False and R is true

5. Homogeneous solution of: y(n) -9/16y(n-2) = x(n-1)
a) C1(3/4)n+C2(3/4)-n
b) C1-(3/4)n-1+C2(3/4)n-1
c) C1(3/4)n
d) C1-(3/4)n

6. Final value theorem is used for:
a) All type of systems
b) Stable systems
c) Unstable systems
d) Marginally stable systems

7. The z-transform corresponding to the Laplace transform G(s) =10/s(s+5) is

a)

b)

c)

d

8. If the z transform of x(n) is X(z) =z(8z-7)/4z2-7z+3, then the final value theorem is :
a) 1
b) 2
c) ∞
d) 0

9. If the z-transform of the system is given by
H (z) = a+z-1/1+az-1
Where a is real valued:
a) A low pass filter
b) A high pass filter
c) An all pass filter
d) A bandpass filter

10. The system is stable if the pole of the z-transform lies inside the unit circle
a) True
b) False