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Alpha Parameters
It is customary in the wave digital filter literature to define the
alpha parameters as
![$\displaystyle \fbox{$\displaystyle \alpha_i \isdef \frac{2\Gamma _i}{\sum_{j=1}^N \Gamma _j}$} \qquad\mbox{(Alpha Parameters)} \protect$](img4896.png) |
(F.14) |
where
are the admittances of the wave digital
element interfaces (or ``reference admittances,'' in WDF terminology).
In terms of the alpha parameters, the force-wave parallel adaptor
performs the following computations:
![$\displaystyle f_J(n)$](img4898.png) |
![$\displaystyle =$](img241.png) |
(Common Junction Force)![$\displaystyle \protect$](img2254.png) |
(F.15) |
![$\displaystyle f^{{-}}_i(n)$](img4900.png) |
![$\displaystyle =$](img241.png) |
(Outgoing Force Waves)![$\displaystyle \protect$](img2254.png) |
(F.16) |
We see that
multiplies and
additions are required.
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