Buchla Waveshapers

**Figure 18:** (left) Original hardware version of Buchla 259 Waveshaper; (right) Virtual analog software version of Buchla 259.

A special nonlinearity associated with West Coast Synthesis and Don Buchla is shown in Fig. 19.

Figure 19: Buchla 259 waveshaper characteristic curve.
$\begin{figure}\begin{center} \epsfig{file=figures/buchla259.eps, width=3.0in} \end{center} \end{figure}$
The characteristic curve is created as:

$\displaystyle y(t) =\begin{cases}x(t), & \vert x(t)\vert \leq 1 \\ x(t) - 2 \mbox{sign}(x(t)), & \vert x(t)\vert > 1 \end{cases}$
Another special nonlinearity associated with Buchla is a “deadband” nonlinearity, shown in Fig. 20.

Figure 20: Deadband waveshaper characteristic curve.
$\begin{figure}\begin{center} \epsfig{file=figures/deadband.eps, width=3.0in} \end{center} \end{figure}$
This characteristic curve is created as:

$\displaystyle y(t) =\begin{cases}0, & \vert x(t)\vert \leq b \\ c \cdot x(t) - c \cdot b \cdot \mbox{sign}(x(t)), & \vert x(t)\vert > b, \end{cases}$
where controls the width of the deadband along the axis and controls the slope of the line segments outside that region.