Matched Z-transform method

Summary

The matched Z-transform method turns a continuous-time filter with a rational transfer function into a discrete-time filter. It sends each pole and each zero $a$ in the $s$-plane to the point $e^{aT}$ in the $z$-plane, where $T$ is the sampling period. Then it fixes the overall gain. It is also called the pole–zero mapping method. It keeps the poles exactly where sampling puts them, and it is simple to apply, but it can distort the frequency response.