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Compare the nature of ROC of z transform and Laplace transform.

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 04

Year : MAY 2015

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Z-transform:

  1. The ROC of X(z) of a two sided signal consists of a ring in the z-plane centered about the origin.

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  1. $σ_1$ and $σ_2$ depend only on magnitude of z.

  2. As in the case of Laplace transform $σ_2 \Rightarrow ∞ $ for a right-sided sequence and $σ_1\Rightarrow 0$ for a left-sided sequence.

  3. If x[n] is two-sided, the ROC will consist of a ring with both $σ_1$ and $σ_2$ finite and non-zero.

Laplace transform:

  1. The ROC of the Laplace transform X(s) of a two sided signal lies between two vertical lines in the s-plane.

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  1. $σ_1$ and $σ_2$ depend only on real part of s.

  2. For a right-sided signal $σ_2\Rightarrow ∞$ and the corresponding ROC is referred to as right-half plane.

  3. Similarly for a left-sided signal $σ_1\Rightarrow ∞$. This ROC is referred to as left-half plane.

  4. When x(t) is two-sided i.e. of infinite extent for both $t \gt 0$ and $t \lt 0 ;$ both $σ_1$ and $σ_2$ are finite and the ROC thus turns out to be a vertical strip in the s-plane.

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