# Region of Convergence Properties

Updated on 2017/07/28 19:26

## Region of Convergence Properties

ROC Region of Convergence -

Definition: ROC is the set of all values of z for which X(Z) will have finite value.

Before going to ROC properties, first it is necessary to study ROC for finite and infinite duration sequences.

### ZT and ROC for finite duration sequence

a) Right handed / Positive /causal sequence-

e.g. x[n] = [1 (origin),  2,  5,  7,  0,  1]

Solution: X(z) = 1 + 2z-1+ 5z-2 + 7z-3 + z-5,

ROC: entire z plane  except z = 0

b) Left handed / Negative /Anti-causal sequence-

c) Both sided sequence -

### ZT and ROC for infinite duration sequence

a) Right handed / Positive /causal sequence-

b) Left handed / Negative /Anti-causal sequence-

c) Both sided sequence -

### Properties of ROC

ROC is a ring or disk centered at the origin.

ROC must be a connected region.

## References

• WikiNote Foundation
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Created by PRIYANKA BHOSALE on 2017/07/26 22:32

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