The simplest case is a complex one-pole resonator having its single pole at :
The maximum gain is readily found to be , i.e., it is obtained at the radian frequency . We therefore define the imaginary part of the pole as the resonance frequency.
Next, we need to find the 3dB-bandwidth. Without loss of generality, we can set , since bandwidth is not changed for a complex one-pole resonator by a vertical translation along the axis. (Consider the graphical method for calculating amplitude response from poles and zeros.) It is now easy to see that the -3dB points of a ``dc resonance are at :
We have thus found that the of a complex one-pole resonator with pole at is given by