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Question

# For a signal x(n)=2nu(n)âˆ’4n u(âˆ’nâˆ’1) 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.⟷zz−a ROC:|z|>a −anu(−n−1)Z.T.⟷zz−a ROC:|z|>a So z-transform of total signal for given ROC is zz−2+zz−4

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