### A generalized 3-d resonator model for simulation of non rectangular shapes

A rectangular enclosure has such an even distribution of resonances that it can be accurately modeled using a feedback delay network, but a non rectangular shape such as a sphere has resonances that are distributed according to the extremal points of the spherical Bessel functions. This work proposes an extension of the already known feedback delay network structure to model a non rectangular shape such as a sphere. A speci c frequency distribution of resonances can be approximated, up to a certain frequency, by inserting an allpass lter of moderate order after the delay line within the comb lter structure. The feedback delay network used for rectangular boxes is therefore augmented with a set of allpass lters allowing parametric control over the enclosure size and the boundary properties. This work was motivated by informal listening tests which have shown that it is possible to identify a basic shape just from the distribution of its audible resonances.