Constant Resonance Gain
It turns out it is possible to normalize
exactly the
resonance gain of the secondorder
resonator tuned by a
single coefficient [
89]. This is accomplished by
placing the two zeros at
, where
is the radius of
the complexconjugate
pole pair . The
transfer function numerator
becomes
, yielding
the total transfer function
which corresponds to the
difference equation
We see there is one more multiplyadd per sample (the term
)
relative to the unnormalized
twopole resonator of Eq.
(
B.13).
The resonance gain is now
Thus, the gain at resonance is
for all resonance tunings
.
Figure
B.19 shows a family of
amplitude responses for the
constant resonancegain twopole, for various values of
and
. We see an excellent improvement in the regularity of the
amplitude response as a function of tuning.
Figure:
Frequency response overlays for the constant
resonancegain twopole filter
,
for and 10 values of
uniformly spaced from 0 to . The 5th case is
plotted using thicker lines.

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