Test: Z Transform


Test Description

15 Questions MCQ Test Digital Signal Processing | Test: Z Transform

Test: Z Transform for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: Z Transform questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Z Transform MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Z Transform below.
Solutions of Test: Z Transform questions in English are available as part of our Digital Signal Processing for Electrical Engineering (EE) & Test: Z Transform solutions in Hindi for Digital Signal Processing course. Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free. Attempt Test: Z Transform | 15 questions in 10 minutes | Mock test for Electrical Engineering (EE) preparation | Free important questions MCQ to study Digital Signal Processing for Electrical Engineering (EE) Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you?
Test: Z Transform - Question 1

The Z-Transform X(z) of a discrete time signal x(n) is defined as:

Detailed Solution for Test: Z Transform - Question 1

Explanation: The z-transform of a real discrete time sequence x(n) is defined as a power of ‘z’ which is equal to , where ‘z’ is a complex variable.

Test: Z Transform - Question 2

 What is the set of all values of z for which X(z) attains a finite value?

Detailed Solution for Test: Z Transform - Question 2

Explanation: Since X(z) is a infinite power series, it is defined only at few values of z. The set of all values of z where X(z) converges to a finite value is called as Radius of Convergence(ROC).

Test: Z Transform - Question 3

 What is the z-transform of the finite duration signal
  

Detailed Solution for Test: Z Transform - Question 3

Explanation: We know that, for a given signal x(n) the z-transform is defined as
Substitute the values of n from -2 to 3 and the corresponding signal values in the above formula
We get, X(z) = 2z2 + 4z + 5 +7z-1 + z-3.

Test: Z Transform - Question 4

 What is the ROC of the signal x(n)=δ(n-k),k>0?

Detailed Solution for Test: Z Transform - Question 4

Explanation: We know that, the z-transform of a signal x(n) is 
Given x(n)= δ(n-k)=1 at n=k
=> X(z)=z-k
From the above equation, X(z) is defined at all values of z except at z=0 for k>0.
So ROC is defined as Entire z-plane, except at z=0.

Test: Z Transform - Question 5

 

 What is the z-transform of the signal x(n)=(0.5)nu(n)?

  

Detailed Solution for Test: Z Transform - Question 5

Explanation: For a given signal x(n), its z-transform 
 

Test: Z Transform - Question 6

Which of the following series has an ROC as mentioned below?
  

Detailed Solution for Test: Z Transform - Question 6

Explanation:
Let x(n)= αnu(n)

Test: Z Transform - Question 7

Find the Z-transform of δ(n + 3).

Detailed Solution for Test: Z Transform - Question 7

Given x(n) = δ(n + 3)
We know that δ(n + 3) =

 

Test: Z Transform - Question 8

What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)?

Detailed Solution for Test: Z Transform - Question 8

Explanation: We know that,

ROC of z-transform of a<sup>n</sup>u(n) is |z|>|a|. ROC of z-transform of b<sup>n</sup>u(-n-1) is |z|<|b|. By combining both the ROC's we get the ROC of z-transform of the signal x(n) as |a|<|z|<|b|

Test: Z Transform - Question 9

What is the ROC of z-transform of finite duration anti-causal sequence?

Detailed Solution for Test: Z Transform - Question 9

Explanation: Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z2 which has a finite value at all values of ‘z’ except at z=∞.So, ROC of an anti-causal sequence is entire z-plane except at z=∞.

Test: Z Transform - Question 10

 What is the ROC of z-transform of an two sided infinite sequence?

Detailed Solution for Test: Z Transform - Question 10

Explanation: Let us plot the graph of z-transform of any two sided sequence which looks as follows.

From the above graph, we can state that the ROC of a two sided sequence will be of the form r2 < |z| < r1.

Test: Z Transform - Question 11

The z-transform of a sequence x(n) which is given as  is known as: 

Detailed Solution for Test: Z Transform - Question 11

Explanation: The entire timing sequence is divided into two parts n=0 to ∞ and n=-∞ to 0.
Since the z-transform of the signal given in the questions contains both the parts, it is called as Bi-lateral z-transform.

Test: Z Transform - Question 12

 What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?

Detailed Solution for Test: Z Transform - Question 12

 

Explanation: A discrete time LTI is BIBO stable, if and only if its impulse response h(n) is absolutely summable. That is,

Test: Z Transform - Question 13

The ROC of z-transform of any signal cannot contain poles. 

Detailed Solution for Test: Z Transform - Question 13

Explanation: Since the value of z-transform tends to infinity, the ROC of the z-transform does not contain poles.

Test: Z Transform - Question 14

Is the discrete time LTI system with impulse response h(n)=an(n) (|a| < 1) BIBO stable?

Detailed Solution for Test: Z Transform - Question 14

Explanation:

Given h(n)= a<sup>n</sup>(n) (|a|<1) The z-transform of h(n) is H(z)=z/(z-a),ROC is |z|>|a| If |a|<1, then the ROC contains the unit circle. So, the system is BIBO stable

Test: Z Transform - Question 15

What is the ROC of a causal infinite length sequence?

Detailed Solution for Test: Z Transform - Question 15

Explanation: The ROC of causal infinite sequence is of form |z|>r1 where r1 is largest magnitude of poles.

3 videos|50 docs|54 tests
Use Code STAYHOME200 and get INR 200 additional OFF
Use Coupon Code
Information about Test: Z Transform Page
In this test you can find the Exam questions for Test: Z Transform solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Z Transform, EduRev gives you an ample number of Online tests for practice