## 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.

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Unstable Poles--Unit Circle Viewpoint

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Bandwidth of One Pole