Time-domain synthesis of conical bore instrument sounds

Model Approaches:

The digital waveguide implementation of a conic frustum:

**Figure 8:** A closed-open conic structure (top) and its digital waveguide block diagram (bottom).
$\begin{figure}\begin{center} \begin{picture}(2.8,2) \put(0.05,0.13){\epsfig{fi... ...esize$\mathcal{R}_{o}$} \end{picture} \end{center} \vspace{-0.2in} \end{figure}$

For a rigidly terminated input (infinite load impedance), the pressure-wave reflectance is given by:

$\begin{displaymath} \mathcal{R}_{o}(z) \stackrel{\Delta}{=} \frac{P^{-}_{o}(z)}{... ...pace{0.1in} a_{1} = \frac{c - \alpha x_{o}}{c + \alpha x_{o}}, \end{displaymath}$

and $\alpha$ is the bilinear transform constant which controls frequency warping.