First-Order Delay-Filter Design

Jot used first-order loss filters for each delay line:

$$H_i(z) = g_i \frac{1-a_i}{1-a_iz^{-1}}$$

• $g_i$ gives desired reverberation time at dc
• $a_i$ sets reverberation time at high frequencies

Design formulas:

$$\begin{eqnarray*} g_i &=& 10^{-3 M_i T / t_{60}(0)}\\ a_i &=& \frac{\mbox{ln}(10)}{4}\log_{10}(g_i)\left(1-\frac{1}{\alpha^2}\right) \end{eqnarray*}$$

where

$$\alpha \mathrel{\stackrel{\Delta}{=}}\frac{t_{60}(\pi/T)}{t_{60}(0)}$$