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