Inst ToolsInst ToolsInst Tools
  • Courses
  • Automation
    • PLC
    • Control System
    • Safety System
    • Communication
    • Fire & Gas System
  • Instrumentation
    • Design
    • Pressure
    • Temperature
    • Flow
    • Level
    • Vibration
    • Analyzer
    • Control Valve
    • Switch
    • Calibration
    • Erection & Commissioning
  • Interview
    • Instrumentation
    • Electrical
    • Electronics
    • Practical
  • Q&A
    • Instrumentation
    • Control System
    • Electrical
    • Electronics
    • Analog Electronics
    • Digital Electronics
    • Power Electronics
    • Microprocessor
Search
  • Books
  • Software
  • Projects
  • Process
  • Tools
  • Basics
  • Formula
  • Power Plant
  • Root Cause Analysis
  • Electrical Basics
  • Animation
  • Standards
  • 4-20 mA Course
  • Siemens PLC Course
Reading: The Z-Transfer Function
Share
Notification Show More
Font ResizerAa
Inst ToolsInst Tools
Font ResizerAa
  • Courses
  • Design
  • PLC
  • Interview
  • Control System
Search
  • Courses
  • Automation
    • PLC
    • Control System
    • Safety System
    • Communication
    • Fire & Gas System
  • Instrumentation
    • Design
    • Pressure
    • Temperature
    • Flow
    • Level
    • Vibration
    • Analyzer
    • Control Valve
    • Switch
    • Calibration
    • Erection & Commissioning
  • Interview
    • Instrumentation
    • Electrical
    • Electronics
    • Practical
  • Q&A
    • Instrumentation
    • Control System
    • Electrical
    • Electronics
    • Analog Electronics
    • Digital Electronics
    • Power Electronics
    • Microprocessor
Follow US
All rights reserved. Reproduction in whole or in part without written permission is prohibited.
Inst Tools > Blog > Multiple Choice Questions > The Z-Transfer Function

The Z-Transfer Function

Last updated: November 27, 2021 5:40 pm
Editorial Staff
Multiple Choice Questions
No Comments
Share
7 Min Read
SHARE

The Z-Transfer Function

1. Consider the following statements regarding a linear discrete-time system:
H (z) = z2+1/(z+0.5)(z-0.5)
1. The system is stable
2. The initial value of h(0) of the impulse response is -4
3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency
Which of these statements are correct?

a) 1,2 and 3
b) 1 and 2
c) 1 and 3
d) 2 and 3

Answer: c

Explanation: Characteristic equation is (z+0.5) (z-0.5) =0
Its root are z =0.5, -0.5
Since both roots are inside the unit circle, hence the system is stable.

2. The minimum number of delay elements required realizing a digital filter with transfer function H (z) =

a) 2
b) 3
c) 4
d) 5

Answer: b

Explanation: H (z) =
Minimum number of delay elements= (Maximum power of z-minimum power of z)
Minimum number of delay elements = 3.

3. A system can be represented in the form of state equations as:
S (n+1) =A S (n) +B x (n)
Y (n) = C S (n) +D x (n)
Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.
H (z) =Y (z)/X (z) is given by:

a) A(ZI – B)-1 C + D
b) B(ZI – C)-1 D + A
c) C(ZI – A)-1 B + D
d) D(ZI – A)-1 C + B

Answer: c

Explanation: Solving both the equations and substituting the value of the output equation into the state equation we get the value of the transfer function as obtained.

4. Assertion (A): The signals anu(n) and anu(-n-1) have the same Z transform, z/(z-a)
Reason (R): the region of convergence of anu(n) is |z|>|a|, whereas the ROC for anu(-n-1) is |z|<|a|.

a) Both A and R are true and R is correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: d

Explanation: Both have the ROC as given in the reason is true but the z transform for the second is with a minus sign.

5. What is the number of roots of the polynomial F(z) = 4z3-8z2-z+2, lying outside the unit circle?

a) 0
b) 1
c) 2
d) 3

Answer: b

Explanation: Factorizing F (z) and then the factors are the roots which here come out to be 3.

6. Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstable
Reason (R): It has an impulse response with a finite number of non-zero samples

a) Both A and R are true and R is correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: d

Explanation: For the system to be stable the value of the transfer function in the discrete time domain must be summable and H[n] calculated is summable hence the system is stable.

7. What is the z-transform of the signal x[n] = anu(n)?

a) X(z) =1/z-1
b) X(z) = 1/1-z
c) X(z) = z/z-a
d) X(z) = 1/z-a

Answer: c

Explanation: By definition this is the basic example of the z-transform and the Z-Transform of the equation is calculated is z/z-a.

8. Which one of the following rules determine the mapping of s-plane to z-plane?

a) Right side of the s-plane maps into outside of the unit circle in z-plane
b) Left half of s-plane maps into inside of the unit circle
c) Imaginary axis in s-plane maps into the circumference of the unit circle
d) All of the mentioned

Answer: d

Explanation: S- plane can be mapped into the z plane with certain rules than right side maps into the outside, left side maps into the inside and imaginary axis maps on the unit circle of the z plane.

9. Assertion (A): The z-transform of the output of the sampler is given by the series.
Reason (R): The relationship is the result of the application of z = e-sT, where T stands for the time gap between the samples.

a) Both A and R are true and R is correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: c

Explanation: T is termed as the time of the sampling instant and z transform is always defined for the instant of the sampling event and this can be as desired by the user.

10. Convolution of two sequences X1[n] and X2[n] are represented by:

a) X1(z)*X2(z)
b) X1(z)X2(z)
c) X1(z)+X2(z)
d) X1(z)/X2(z)

Answer: a

Explanation: Convolution of the two sequences is the combination of multiplication and addition of the two sequences at each instant and convolution in time domain is multiplication in the frequency domain.

Don't Miss Our Updates
Be the first to get exclusive content straight to your email.
We promise not to spam you. You can unsubscribe at any time.
Invalid email address
You've successfully subscribed !

Continue Reading

Mass Spectrometer Questions & Answers
UV Visible Spectrometers Questions and Answers
Concepts of State, State Variables & State Model
Encoder Multiple Choice Questions
Frequency Response MCQ
Polar Plots MCQ
Share This Article
Facebook Whatsapp Whatsapp LinkedIn Copy Link
Share
Leave a Comment

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Stay Connected

128.3kFollowersLike
69.1kFollowersFollow
208kSubscribersSubscribe
38kFollowersFollow

Categories

Explore More

The Z-Transform
Gas Chromatograph- Mass Spectrometer
Carbon Monoxide Questions & Answers
Column Efficiency and Column Resolution Questions and Answers
Level Measurement Multiple Choice Questions
Inductively Coupled Plasma Mass Spectrometer
Single Beam and Double Beam Instruments
Secondary Reference Electrodes Questions & Answers

Keep Learning

Pneumatic Control Mechanisms Objective Questions

Pneumatic Control Mechanisms Objective Questions

Frequency Response MCQ

Bode Plots MCQ

Optimal Control Systems

Parameter Optimization

Time Response Analysis

Robotic Control System – Part I

Analyzers Questions and Answers

Electrochemical Methods for Oxygen Analysis Questions & Answers

Pneumatic Systems Objective Questions

Pneumatic Systems Objective Questions

Time Response Analysis

Steady-state Errors & Error Constants

State Variable Analysis and Design

Controllability & Observability

Learn More

Short Circuit and Open Circuit

Short Circuit and Open Circuit

Free Safety Instrumented System Training Course

Free Safety Instrumented System Training Course

Ground Rod

What is a Ground Rod?

D’Arsonval Movement

D’Arsonval Meter Movement

Turbine Flow Meter

All About Turbine Meters

Basics of Explosion Protection

Basics of Explosion Protection

Needle Valve Schematic

How Needle Valve Works ?

Power Systems Questions & Answers

Power Systems MCQ Series 11

Follow US
All rights reserved. Reproduction in whole or in part without written permission is prohibited.
Welcome Back!

Sign in to your account

Username or Email Address
Password

Lost your password?