## Time Constant of One Pole

A useful approximate formula giving the*decay time-constant*

^{9.4}(in seconds) in terms of a pole radius is

where denotes the sampling interval in seconds, and we assume . The exact relation between and is obtained by sampling an exponential decay:

*samples*is of course . For higher-order systems, the approximate decay time is , where is the largest pole magnitude (closest to the unit circle) in the (stable) system.

**Next Section:**

Unstable Poles--Unit Circle Viewpoint

**Previous Section:**

Bandwidth of One Pole