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Question

For a signal x(n)=2nu(n)4n u(n1) the ROC is defined as a<|z|< b. The correct statement(s) is /are

A
The system is stable
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B
Z -transform of signal is zz2+zz4
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C
The value of a + b = 2
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D
The initial value of theorem is not applicable.
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Solution

The correct option is D The initial value of theorem is not applicable.

(b, c)

ROC is signals is 2<|z|<4

Hence a =2
b = 4
a+b = 6

(b) Initial value theroem is applicable only for causal type signals.
(d) As ROC does not contain unit circle thus system is unstable.

(c) anu(n)Z.T.zza ROC:|z|>a

anu(n1)Z.T.zza ROC:|z|>a

So z-transform of total signal for given ROC is

zz2+zz4

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