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It is customary in the wave digital filter literature to define the
beta parameters as
![$\displaystyle \fbox{$\displaystyle \beta_i \isdef \frac{2R_i}{\sum_{j=1}^N R_j}$} \protect$](img3289.png) |
(N.26) |
where
are the port impedances (attached element reference
impedances). In terms of the beta parameters, the force-wave series
adaptor performs the following computations:
However, we normally employ a mixture of parallel and series adaptors,
while keeping a force-wave simulation. Since
, we obtain, after a small amount of algebra, the following
recipe for the series force-wave adaptor:
We see that we have
multiplies and
additions as in the
parallel-adaptor case. However, we again have from Eq. (N.26) that
so that we may implement one beta parameter as 2 minus the
sum of the rest, thus eliminating a multiplication by creating
a dependent port.
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