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