EXPERIMENTS WITH NON-LINEAR FILTERS Discovering Excitable Regions

We describe the development and implementation of a family of non-linear filters in which the non-linear term is given a variable recursive delay, in the context of a search for what we term an arithmetical instrument – an instrument whose design is founded on purely numerical models. Such filters are inherently unstable; we describe how they may be controlled, not only by the careful selection and constraining of parameters, but also by appropriate and idiomatic performance technique. We draw comparisons between these filters and the behaviour of acoustic instruments, which typically exhibit what we call excitable regions of sonic activity.