Zita-Rev1 Damping Filters

FDN reverberators employ a damping filter for each delay line

Zita-Rev1 three-band damping filter:

$$H_d(z)=H_l(z)H_h(z)$$

where

$$\begin{eqnarray*} H_l(z) &=& g_m + (g_0-g_m)\frac{1-p_l}{2}\frac{1+z^{-1}}{1-p_lz^{-1}} \;=\;\mbox{\emph{low-shelf}}\\ [5pt] H_h(z) &=& \frac{1-p_h}{1-p_hz^{-1}} \;=\;\mbox{\emph{low-pass}} \end{eqnarray*}$$

$$\begin{eqnarray*} g_0 &=& \mbox{Desired gain at dc}\\ [5pt] g_m &=& \mbox{Desired gain across \lq\lq middle frequencies''}\\ [5pt] p_l &=& \mbox{Low-shelf pole controlling low-to-mid crossover:}\\ &\;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;& \frac{1-\pi f_1T}{1+\pi f_1T}\\ [5pt] p_h &=& \mbox{Low-pass pole controlling high-frequency damping:}\\ && \mbox{Gives \emph{half} middle-band $t_{60}$\ at start of \lq\lq high'' band} \end{eqnarray*}$$