Feedback delay networks (FDNs) are recursive filters,which are widely used for artificial reverberation and decorrela-tion. One central challenge in the design of FDNs is the generationof sufficient echo density in the impulse response without compro-mising the computational efficiency. In a previous contribution,we have demonstrated that the echo density of an FDN can beincreased by introducing so-called delay feedback matrices whereeach matrix entry is a scalar gain and a delay. In this contribu-tion, we generalize the feedback matrix to arbitrary lossless filterfeedback matrices (FFMs). As a special case, we propose the velvetfeedback matrix, which can create dense impulse responses at aminimal computational cost. Further, FFMs can be used to emulatethe scattering effects of non-specular reflections. We demonstratethe effectiveness of FFMs in terms of echo density and modaldistribution.

Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. We demonstrate how explicit knowledge of the FDN’s modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that the perceived modal density is considerably lower than the theoretic modal density.