Digital Signal Processing

Rational Z Transform

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What are the values of z for which the value of X(z)=0?
Poles
Zeros
Solutions
None of the mentioned
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).
Question 2
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Pass Ratio : 100%
If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
|N-M| poles at origin(if N>M)
|N+M| zeros at origin(if N>M)
|N+M| poles at origin(if N>M)
|N-M| zeros at origin(if N>M)
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).
Question 3
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Pass Ratio : 100%
)
Explanation:
From the figure given, the z-transform of the signal has 8 zeros on circle of radius ‘a’ and 7 poles at origin.
Question 4
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Pass Ratio : 100%
Which of the following signals have a pole-zero plot as shown below?
a.u(n)
u(an)
anu(n)
none of the mentioned
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.
Question 5
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Pass Ratio : 100%
)
Explanation:
Question 6
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Pass Ratio : 100%
If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
|N-M| poles at origin(if N < M)
|N+M| zeros at origin(if N < M)
|N+M| poles at origin(if N < M)
|N-M| zeros at origin(if N < M)
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).
Question 7
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Pass Ratio : 100%
Which of the following signals have a pole-zero plot as shown below?(Let M=8 in the figure)
Explanation:
Question 8
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Pass Ratio : 100%
)
Explanation:
Question 9
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Pass Ratio : 100%
What are the values of z for which the value of X(z)=∞?
Poles
Zeros
Solutions
None of the mentioned
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).
Question 10
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Pass Ratio : 100%
The z-transform X(z) of the signal x(n)=anu(n) has:
One pole at z=0 and one zero at z=a
One pole at z=0 and one zero at z=0
One pole at z=a and one zero at z=a
One pole at z=a and one zero at z=0
Explanation:
The z-transform of the given signal is X(z)=z/(z-a)