#### 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 .

**Next Section:**

Two-Pole Partial Fraction Expansion

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Trigonometric Identities, Continued