Orthogonalized First-Order Delay-Filter Design
In [217], first-order delay-line filters of the form
![$\displaystyle H_i(z) \eqsp g'_i \frac{1-p_i}{1-p_iz^{-1}}
$](http://www.dsprelated.com/josimages_new/pasp/img874.png)
![$ g_i=g'_i\cdot(1-p_i)$](http://www.dsprelated.com/josimages_new/pasp/img875.png)
![$ H_i(1)=g'_i$](http://www.dsprelated.com/josimages_new/pasp/img876.png)
![$ p_i$](http://www.dsprelated.com/josimages_new/pasp/img301.png)
![$ g'_i$](http://www.dsprelated.com/josimages_new/pasp/img877.png)
![$ p_i$](http://www.dsprelated.com/josimages_new/pasp/img301.png)
![$ \,$](http://www.dsprelated.com/josimages_new/pasp/img196.png)
![$\displaystyle g'_i \eqsp 10^{-3 M_i T / t_{60}(0)}.
$](http://www.dsprelated.com/josimages_new/pasp/img878.png)
![$\displaystyle p_i \eqsp \frac{\mbox{ln}(10)}{4}\log_{10}(g_i)\left(1-\frac{1}{\alpha^2}\right)
$](http://www.dsprelated.com/josimages_new/pasp/img879.png)
denotes the ratio of reverberation time at half the sampling rate divided by the reverberation time at dc.4.16
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