### Constant Resonance Gain

It turns out it is possible to normalize *exactly* the
*resonance gain* of the second-order resonator tuned by a
single coefficient [89]. This is accomplished by
placing the two zeros at
, where is the radius of
the complex-conjugate pole pair . The transfer function numerator
becomes
, yielding
the total transfer function

Thus, the gain at resonance is for all resonance tunings .

Figure B.19 shows a family of amplitude responses for the constant resonance-gain two-pole, for various values of and . We see an excellent improvement in the regularity of the amplitude response as a function of tuning.

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Peak Gain Versus Resonance Gain

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Normalizing Two-Pole Filter Gain at Resonance