The magnitude of a complex pole determines the
damping or bandwidth of the resonator. (Damping may be
defined as the reciprocal of the bandwidth.)

When is close to 1, a reasonable definition of bandwidth is
provided by

(11.4)

(11.5)

where is the pole radius, is the bandwidth in Hertz (cycles
per second), and is the sampling interval in seconds. It can be
shown (§C.6) that under this definition is approximately
equal to the 3-dB bandwidth (or half-power bandwidth)
of the resonator.

Figure 10.7 shows a family of frequency responses for the
two-pole resonator obtained by setting and varying . The
value of , in all cases is , corresponding to
. The analytic expressions for amplitude and phase response are