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Test: Rational Z Transform


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10 Questions MCQ Test Digital Signal Processing | Test: Rational Z Transform

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

What are the values of z for which the value of X(z)=0?

Detailed Solution for Test: Rational Z Transform - Question 1

Explanation: For a rational z-transform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).

Test: Rational Z Transform - Question 2

What are the values of z for which the value of X(z)=∞?

Detailed Solution for Test: Rational Z Transform - Question 2

Explanation: For a rational z-transform X(z) to be infinity, the denominator of X(z) is zero and the solutions of the denominator are called as ‘poles’ of X(z).

Test: Rational Z Transform - Question 3

 If X(z) has M finite zeros and N finite poles, then which of the following condition is true?

Detailed Solution for Test: Rational Z Transform - Question 3

Explanation: If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z -M+N.X'(z).
So, if N>M then z has a positive power. So, it has |N-M| zeros at origin.

Test: Rational Z Transform - Question 4

If X(z) has M finite zeros and N finite poles, then which of the following condition is true?

Detailed Solution for Test: Rational Z Transform - Question 4

Explanation: If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z-M+N.X'(z).
So, if N < M then z has a negative power. So, it has |N-M| poles at origin.

Test: Rational Z Transform - Question 5

Which of the following signals have a pole-zero plot as shown below?

Detailed Solution for Test: Rational Z Transform - Question 5

Explanation: From the given pole-zero plot, the z-transform of the signal has one zero at z=0 and one pole at z=a.
So, we obtain X(z)=z/(z-a)
By applying inverse z-transform for X(z), we get
x(n)= anu(n).

Test: Rational Z Transform - Question 6

Which of the following signals have a pole-zero plot as shown below?(Let M=8 in the figure)

Detailed Solution for Test: Rational Z Transform - Question 6

Explanation: From the figure given, the z-transform of the signal has 8 zeros on circle of radius ‘a’ and 7 poles at origin.

Test: Rational Z Transform - Question 7

 The z-transform X(z) of the signal x(n)=anu(n) has:

Detailed Solution for Test: Rational Z Transform - Question 7

Explanation: The z-transform of the given signal is X(z)= z/(z-a)
So, it has one pole at z=a and one zero at z=0.

Test: Rational Z Transform - Question 8

 What is the nature of the signal whose pole-zero plot is as shown?

Detailed Solution for Test: Rational Z Transform - Question 8

Explanation: From the pole-zero plot, it is shown that r < 1, so the signal is a decaying signal.

Test: Rational Z Transform - Question 9

What are the values of z for which the value of X(z)=0?

Detailed Solution for Test: Rational Z Transform - Question 9

Explanation: For a rational z-transform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).

Test: Rational Z Transform - Question 10

 If Y(z) is the z-transform of the output function, X(z) is the z-transform of the input function and H(z) is the z-transform of system function of the LTI system, then H(z)=?

Detailed Solution for Test: Rational Z Transform - Question 10

Explanation: We know that for an LTI system, y(n)=h(n)*x(n)
On applying z-transform on both sides we get, Y(z)=H(z).X(z)=>H(z)= ( Y(z))/(X(z) ).

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