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Signals and systems electrical engineering miscellaneous

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Signals and systems electrical engineering miscellaneous
  1. If x[n] =
    1
    		|n| -
    1
    		|n|u[n],
    32

    then the region of conver gence (ROC) of its Z-transform in the Z-plane will be
    1. 1
      		 < |z| < 3
      3
    2. 1
      		 < |z| <
      1
      32
    3. 1
      		 < |z| > 3
      2
    4. 1
      		 < |z|
      3
Correct Option: C

x(n) =
1
|n| -
1
n + u[n]
32

=
1
n u(n) +
1
-nu(-n) -
1
n u(n)
332

=
1
n u(n) + (3)n u(-n) -
1
n u(n)
32

ROC : |z| >
1
     |z| < 3
3

|z| >
1
2

Common ROC :
1
 < |z| < 3
2


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