### Normalizing Two-Pole Filter Gain at Resonance

The question we now pose is how to best compensate the*tunable*two-pole resonator of §B.1.3 so that its peak gain is the same for all tunings. Looking at Fig.B.17, and remembering the graphical method for determining the amplitude response,

^{B.6}it is intuitively clear that we can help matters by adding two

*zeros*to the filter, one near dc and the other near . A zero exactly at dc is provided by the term in the transfer function numerator. Similarly, a zero at half the sampling rate is provided by the term in the numerator. The series combination of both zeros gives the numerator . The complete second-order transfer function then becomes

Checking the gain for the case , we have

**Next Section:**

Constant Resonance Gain

**Previous Section:**

DC Blocker Software Implementations