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Test: One Sided Z Transform


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10 Questions MCQ Test Digital Signal Processing | Test: One Sided Z Transform

Test: One Sided Z Transform for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: One Sided Z Transform questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: One Sided 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: One Sided Z Transform below.
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Test: One Sided Z Transform - Question 1

The z-transform of a signal x(n) whose definition is given byis known as: 

Detailed Solution for Test: One Sided Z Transform - Question 1

Explanation: The z-transform of the x(n) whose definition exists in the range n=-∞ to +∞ is known as bilateral or two sided z-transform. But in the given question the value of n=0 to +∞. So, such a z-transform is known as Unilateral or one sided z-transform.

Test: One Sided Z Transform - Question 2

For what kind of signals one sided z-transform is unique?

Detailed Solution for Test: One Sided Z Transform - Question 2

Explanation: One sided z-transform is unique only for causal signals, because only these signals are zero for n<0.

Test: One Sided Z Transform - Question 3

 What is the one sided z-transform X+(z) of the signal x(n)={1,2,5,7,0,1}? 

Detailed Solution for Test: One Sided Z Transform - Question 3

Explanation: Since the one sided z-transform is valid only for n>=0, the z-transform of the given signal will be X+(z)= 5+7z-1+z-3.

Test: One Sided Z Transform - Question 4

What is the one sided z-transform of x(n)=δ(n-k)?

Detailed Solution for Test: One Sided Z Transform - Question 4

Explanation: Since the signal x(n)= δ(n-k) is a causal signal i.e., it is defined for n>0 and x(n)=1 at z=k
So, from the definition of one sided z-transform X+(z)=z-k.

Test: One Sided Z Transform - Question 5

What is the one sided z-transform of x(n)=δ(n+k)?

Detailed Solution for Test: One Sided Z Transform - Question 5

Explanation: Since the signal x(n)= δ(n+k) is an anti causal signal i.e., it is defined for n<0 and x(n)=1 at z= -k. Since the one sided z-transform is defined only for causal signal, in this case X+(z)=0.

Test: One Sided Z Transform - Question 6

 If X+(z) is the one sided z-transform of x(n), then what is the one sided z-transform of x(n-k)?

Detailed Solution for Test: One Sided Z Transform - Question 6

Explanation: From the definition of one sided z-transform we have,

Test: One Sided Z Transform - Question 7

 If x(n)=an, then what is one sided z-transform of x(n-2)?

Detailed Solution for Test: One Sided Z Transform - Question 7

Explanation:

Test: One Sided Z Transform - Question 8

If x(n)=an, then what is one sided z-transform of x(n+2)?

Detailed Solution for Test: One Sided Z Transform - Question 8

Explanation: We will apply the time advance theorem with the value of k=2.We obtain,

Test: One Sided Z Transform - Question 9

If X+(z) is the one sided z-transform of the signal x(n), then lim┬(n→∞)x(n)=lim┬(z→1)(z-1) X+ (z) is called Final value theorem. 

Detailed Solution for Test: One Sided Z Transform - Question 9

Explanation: In the above theorem, we are calculating the value of x(n) at infinity, so it is called as final value theorem.

Test: One Sided Z Transform - Question 10

The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞? 

Detailed Solution for Test: One Sided Z Transform - Question 10

Explanation: The step response of the system is y(n)=x(n)*h(n) where x(n)=u(n)
On applying z-transform on both sides, we get

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