Resonator Bandwidth in Terms of Pole Radius
The magnitude of a complex pole determines the damping or bandwidth of the resonator. (Damping may be defined as the reciprocal of the bandwidth.)
As derived in §8.5, when is close to 1, a reasonable
definition of 3dB-bandwidth is provided by
where is the pole radius, is the bandwidth in Hertz (cycles per second), and is the sampling interval in seconds.
Figure B.6 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
where and .
Two-Pole Partial Fraction Expansion
Trigonometric Identities, Continued