#### 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

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Two-Pole Partial Fraction Expansion

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Trigonometric Identities, Continued