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 nonrectangular 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.
Highlights
The feedback delay network (FDN) of order N, as depicted in Figure 1 for N = 4, is the multivariable generalization of the recursive comb filter, and it has been widely used to simulate the late reverbation of an enclosure [1, 2, 3, 4]
The delay lengths of an FDN are sometimes chosen with number-theoretic considerations in order to minimize the overlapping of echoes, as it was done with classic reverberation structures [6]
Since any harmonic series of resonances can be reproduced by means of a recursive comb filter, a reference FDN can be constructed as a parallel connection of comb filters or, in other words, with a diagonal feedback matrix
Summary
Some energy gets transferred from one mode to another due to nonmirror reflection at the walls This effect is called diffusion [5] and is encompassed by the nondiagonal elements of the feedback matrix. A prior realization of the spherical resonator, depicted, exploited the fact that the extremal points are asymptotically equidistant, using recursive comb filters with feedback highpass filters to reproduce the medium- and high-frequency resonances [9]. A set of low-frequency resonances were individually reproduced by tuned secondorder resonant filters Such prior realization was successfully experimented in the AML, Architecture and Music Laboratory, a museum installation where the visitor can experience how shapes such as, e.g. a tube, a cube or a sphere imprint a specific signature on the sounds. We indicate how the simulation of cylinders of various lengths and radii might be achieved by the same structure with the proper parameter design
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