Pole mapping

A very simple method is to simply map poles from the left-half $s$ plane to the unit circle in the $z$ plane via

$$z_i = e^{s_i T}$$

where $s_i$ is the location of the $i$th pole. After mapping the poles in this way, zeros can be computed in a variety of ways, such as using Prony's method [455, Section G.4.4],[279,298].