Optimization Approaches for Feedback Delay Networks

Sammanfattning: Feedback delay networks are systems based on a set of delay lines whose outputs get fed back into each others inputs. This kind of architecture is mainly used to provide a system for artificial reverberation, that is, a system to emulate the prolonging of sound in a physical space. Two sets of parameters of a feedback delay network heavily influence how well the system does in terms of accomplishing perceptually convincing reverberation: the lengths of the delay lines and the feedback matrix, containing the gains of the feedback paths. In this thesis, we propose three different metrics that attempt to quantify how convincing the impulse response from a feedback delay network is, in terms of imitating real-world reverberation. These metrics are then applied to a feedback delay network together with a set of parameterizable rotation matrices. More specifically, by fixing the delays in different configurations, optimization procedures over the set of rotation matrices are performed with respect to the three metrics. The optimal matrices are then compared with some popular feedback matrices from the literature, as well as the least optimal matrices. Furthermore, the mixing time of the feedback delay network over the set of rotation matrices is calculated in the different configurations. The results from the optimization procedures are then evaluated partly subjectively by listening to impulse responses. The results suggest that two of the three different metrics might be useful for finding feedback matrices that contribute to producing perceptually convincing impulse responses. The findings also suggest that the matrices that produce a fast build-up of echo density in the feedback delay network coincide with the matrices that perform well with respect to the three metrics.