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Quiz: DSP - Z Transform

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Number of Questions: 24

Question: 6 -

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

Options:

r₂<|z|<r₁

None of the mentioned

|z|<r₁

|z|>r₁

Answer:

r₂<|z|<r₁

Solution not available.

Question: 7 -

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

Options:

|a|<|z|>|b|

|a|>|z|>|b|

|a|>|z|<|b|

|a|<|z|<|b|

Answer:

|a|<|z|<|b|

Solution:

ROC of z-transform of aⁿu(n) is |z|>|a|.
ROC of z-transform of bⁿu(-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|.

Question: 8 -

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

Options:

z=0

Entire z-plane, except at z=0

Entire z-plane, except at z=∞

z=∞

Answer:

Entire z-plane, except at z=∞

Solution:

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=∞.

Question: 9 -

What is the ROC of a causal infinite length sequence?

Options:

|z|<r₁

r₂<|z|<r₁

None of the mentioned

|z|>r₁

Answer:

|z|>r₁

Solution:

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

Question: 10 -

The z-transform of a sequence x(n) which is given as X(z)=∑_n=−_∞^∞x(n) z⁻ⁿ is known as _____________

Options:

Bi-lateral Z-transform

Tri-lateral Z-transform

None of the mentioned

Uni-lateral Z-transform

Answer:

Bi-lateral Z-transform

Solution:

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.

Quiz: DSP - Z Transform

Solution not available.

Solution: ROC of z-transform of anu(n) is |z|>|a|.ROC of z-transform of bnu(-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|.

Solution: 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=∞.

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

Solution: 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.

Solution:

ROC of z-transform of aⁿu(n) is |z|>|a|.
ROC of z-transform of bⁿu(-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|.

Solution:

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=∞.

Solution:

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

Solution:

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.