# The Z-Transform MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Z-Transform”.

1. The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor

a) α

b) 1/α

c) α^{2}

d) α

2. Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are

a) The same

b) Reciprocal of each other

c) Negative of each other

d) Complements of each other

3. The discrete-time signal x (n) = (-1)^{n} is periodic with fundamental period

a) 6

b) 4

c) 2

d) 0

4. The ROC of z-transform of the discrete time sequence x(n) = is:

a) 1/3>|z|<1/2

b) |z|>1/2

c) |z|<1/3

d) 2>|z|<3

5. The region of convergence of the z-transform of a unit step function is:

a) |z|>1

b) |z|<1

c) (Real part of z)>0

d) (Real part of z)<0

6. A sequence x (n) with the z-transform X (z) = Z^{4} + Z^{2} – 2z + 2 – 3Z^{-4} is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:

a) -6

b) Zero

c) 2

d) -4

7. Which one of the following is the correct statement? The region of convergence of z-transform of x[n] consists of the values of z for which x[n] is:

a) Absolutely integrable

b) Absolutely summable

c) Unity

d) <1

8. If the region of convergence of x1[n]+x2[n] is 1/>|z|<2/3, the region of convergence of x1[n]-x2[n] includes:

a) 1/3>|z|<3

b) 2/3>|z|<3

c) 3/2>|z|<3

d) 1/3>|z|<2/3

9. H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:

a) Poles must be inside the unit circle and zeros must be outside the unit circle

b) Poles and zeroes must be inside the unit circle

c) Poles and zeroes must be outside the unit circle

d) Poles must be outside the unit circle and zeros must be inside the unit circle

10. Z and Laplace transform are related by:

a) s = ln z

b) s =ln z/T

c) s =z

d) s= T/ln z