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Practical FDN Design

In our experience, given an FDN reverberator structure, setting the delay lengths can be a rather tedious job. The vast majority of possible delays just provide poor results in the sense that the time response is too ``rough'' or the frequency response is too ``colored.'' An interesting approach to this problem might be to use nonlinear optimization techniques such as ``simulated annealing'' or ``genetic algorithms'' to optimize the delay lengths such that ``perceptual uniformity'' of the response is maximized in the time and frequency domains jointly.

Designing the delay lengths from room geometry has the property of giving a reverberator which is always consistent with a desired room in that the low-frequency modes are matched. However, there does not seem to be any compelling reason to match specific low-frequency mode tunings. Noticeable room resonances are normally perceived as defects in a listening space. Early reflections, on the other hand, contribute strongly to the perceived ``spatial impression'' [2]. In other applications, however, such as modeling the soundboard of a piano as a reverberator, the specific coloring or ``equalization'' provided by the reverberator is important and must be preserved. In such applications, it is normally necessary to match low-frequency resonances accurately and high-frequency resonances only statistically.

When the FDN order is large (larger than 8 for satisfactory results), poor results can still be obtained when modeling desired room dimensions which are not favorable. In fact, even for the shoe-box room shape, the relative dimensions play a very important role in determining the smoothness of the reverb [15]. Of course, diffusion contributes significant smoothing to the response, so full feedback matrices (as opposed to diagonal feedback matrices) are especially needed to achieve good reverberators using low-order FDNs.

On balance, it seems that what is needed for good reverberator design in general is

precise matching of early reflections,
minimal coloration due to uneven mode distributions in the frequency domain,
an appropriate smoothly declining decay-time versus frequency, and
smooth, rich echo density late in the impulse response, having no noticeable patterns.

These desiderata indicate that, rather than attempting to model real rooms, lossless prototype FDNs optimizing criteria (2) and (4) should be found, for a given order, which have at least one delay line long enough to support injection of specific early reflections to satisfy (1), and then lowpass filters as in (21) should be added to satisty criterion (3). The main open issue is how the optimization of (2) and (4) should best be carried out for specific classes of structurally lossless feedback matrices.

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``Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation'', by Davide Rocchesso and Julius O. Smith III, preprint of version in IEEE Transactions on Speech and Audio, vol. 5, no. 1, pp. 51-60, Jan. 1996.

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Copyright © 2005-03-10 by Davide Rocchesso and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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