# 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) = z^{3}-2z^{2}+z/z^{2}+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) z^{2}/(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)/4z^{2}-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