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Test: Z Transform Properties - 1


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10 Questions MCQ Test Digital Signal Processing | Test: Z Transform Properties - 1

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

Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].

Detailed Solution for Test: Z Transform Properties - 1 - Question 1

Explanation: According to the linearity property of z-transform, if X(z) and Y(z) are the z-transforms of x(n) and y(n) respectively then, the z-transform of x(n)+y(n) is X(z)+Y(z).

Test: Z Transform Properties - 1 - Question 2

What is the z-transform of the signal x(n)=[3(2n)-4(3n)]u(n)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 2

Explanation: Let us divide the given x(n) into x1(n)= 3(2n)u(n) and x2(n)= 4(3n)u(n)
and x(n)=x1(n)-x2(n)
From the definition of z-transform X1(z)= 3/(1-2z-1) and X2(z)= 4/(1-3z-1)
So, from the linearity property of z-transform
X(z)=X1(z)-X2(z)
=> X(z)= 3/(1-2z-1)-4/(1-3z-1).

Test: Z Transform Properties - 1 - Question 3

What is the z-transform of the signal x(n)=sin(jω0n)u(n)?

Detailed Solution for Test: Z Transform Properties - 1 - Question 3

Explanation: By Euler’s identity, the given signal x(n) can be written as

Test: Z Transform Properties - 1 - Question 4

According to Time shifting property of z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 4

Explanation: According to the definition of Z-transform

Test: Z Transform Properties - 1 - Question 5

What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?

Detailed Solution for Test: Z Transform Properties - 1 - Question 5

Explanation:

Test: Z Transform Properties - 1 - Question 6

 If X(z) is the z-transform of the signal x(n) then what is the z-transform of anx(n)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 6

Explanation: We know that from the definition of z-transform

Test: Z Transform Properties - 1 - Question 7

 If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 7

Explanation: Given ROC of X(z) is r1<|z|<r2
Then ROC of X(a-1z) will be given by r1<|a-1z |<r2=|a|r1<|z|<|a|r2

Test: Z Transform Properties - 1 - Question 8

 What is the z-transform of the signal x(n)=an(sinω0n)u(n)?    

Detailed Solution for Test: Z Transform Properties - 1 - Question 8

Explanation:

Test: Z Transform Properties - 1 - Question 9

 If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 9

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

Test: Z Transform Properties - 1 - Question 10

X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal nx(n)? 

Detailed Solution for Test: Z Transform Properties - 1 - Question 10

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

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