Pole or Zero on the Unit Circle

The general form of the transfer equation for a single zero is

If r = 1, then the zero (or pole) is on the unit circle. In the small frequency limit, the transfer function is

Pole on the Unit Circle (Integrator)

A sharp peak in the magnitude response near a pole is called a resonance.

The bandwidth B, in radians per sample, defined as the separation between the half-square-magnitude points, is given by

For r = 0.999 and a sample frequency of 44 kHz, the bandwidth is 14 Hz.

Maintained by John Loomis, last updated 23 Oct 1997