written 8.0 years ago by | • modified 8.0 years ago |
Mumbai University > EXTC > Sem 4 > Signals and Systems
Marks : 04
Year : MAY 2015
written 8.0 years ago by | • modified 8.0 years ago |
Mumbai University > EXTC > Sem 4 > Signals and Systems
Marks : 04
Year : MAY 2015
written 8.0 years ago by |
Z-transform:
$σ_1$ and $σ_2$ depend only on magnitude of z.
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.
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:
$σ_1$ and $σ_2$ depend only on real part of s.
For a right-sided signal $σ_2\Rightarrow ∞$ and the corresponding ROC is referred to as right-half plane.
Similarly for a left-sided signal $σ_1\Rightarrow ∞$. This ROC is referred to as left-half plane.
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.