When a region of convergence is specified, then causality can be determined.
2.
The theory of such series is trickier than for single-variable series, with more complicated regions of convergence.
3.
Then the Region of convergence is simply the intersection between the four 2D Z-transforms in each quadrant.
4.
In general, the region of convergence for causal systems is not the same as that of anticausal systems.
5.
Therefore, the region of convergence is a half-plane of the form, possibly including some points of the boundary line.
6.
Every power series with a positive radius of convergence is analytic on the interior of its region of convergence.
7.
That is, in the region of convergence can effectively be expressed as the absolutely convergent Laplace transform of some other function.
8.
Unlike other parts of the Himalayan collision, this region of convergence is quite narrow, about 900 miles ( 1, 448 kilometers ).
9.
For that, you may want to look at Laplace transform # Region of convergence and Laplace transform # Table of selected Laplace transforms.
10.
There are several Paley Wiener theorems concerning the relationship between the decay properties of and the properties of the Laplace transform within the region of convergence.
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