Alpha Parameters
It is customary in the wave digital filter literature to define the alpha parameters as
where
![$ \Gamma _i \isdef 1/R_i$](http://www.dsprelated.com/josimages_new/pasp/img4844.png)
We see that
![$ N$](http://www.dsprelated.com/josimages_new/pasp/img20.png)
![$ 2N-1$](http://www.dsprelated.com/josimages_new/pasp/img759.png)
![$ \,$](http://www.dsprelated.com/josimages_new/pasp/img196.png)
![$\displaystyle \sum_{i=1}^N \alpha_i = 2,
$](http://www.dsprelated.com/josimages_new/pasp/img4849.png)
![$ \alpha_1$](http://www.dsprelated.com/josimages_new/pasp/img4850.png)
![$ 2-\sum_{i=2}^N\alpha_i$](http://www.dsprelated.com/josimages_new/pasp/img4851.png)
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It is customary in the wave digital filter literature to define the alpha parameters as