Generalization of a 3-D resonator model for the simulation of spherical enclosures

TL;DR

This paper extends feedback delay networks with allpass filters to accurately model the resonant properties of spherical enclosures, enabling efficient simulation of their acoustic characteristics.

Contribution

It introduces a novel extension of feedback delay networks incorporating allpass filters to model spherical resonances, which was not previously achievable.

Findings

Effective approximation of spherical resonance distribution up to certain frequencies

Parametric control over enclosure size and boundary properties achieved

Potential for shape identification through resonance analysis

Abstract

A rectangular enclosure has such an even distribution of resonances that it can be accurately and efficiently modelled using a feedback delay network. Conversely, a non rectangular shape such as a sphere has a distribution of resonances that challenges the construction of an efficient model. This work proposes an extension of the already known feedback delay network structure to model the resonant properties of a sphere. A specific frequency distribution of resonances can be approximated, up to a certain frequency, by inserting an allpass filter of moderate order after each delay line of a feedback delay network. The structure used for rectangular boxes is therefore augmented with a set of allpass filters 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.