Feedback delay networks (FDNs) are frequently used to generate artificial reverberation. This paper discusses the temporal features of impulse responses produced by FDNs, i.e., the number of echoes per time unit and its evolution over time. This so-called echo density is related to known measures of mixing time and their psychoacoustic correlates such as auditive perception of the room size. It is shown that the echo density of FDNs follows a polynomial function, whereby the polynomial coefficients can be derived from the lengths of the delays for which an explicit method is given. The mixing time of impulse responses can be predicted from the echo density, and conversely, a desired mixing time can be achieved by a derived mean delay length. A Monte Carlo simulation confirms the accuracy of the derived relation of mixing time and delay lengths.

Of the many available reverberation time prediction formulas, Sabine's and Eyring's equations are still widely used. The assumptions of homogeneity and isotropy of sound energy during the decay associated with those models are usually recognized as a reason for lack of agreement between predictions and measurements. At the same time, the inaccuracy in the estimation of the sound-absorption coefficient adds to the uncertainty of calculations. This paper shows that the error of incorrectly assumed sound absorption is more detrimental to the prediction precision than the inherent error in the formulas themselves. The proposed absorption calibration procedure reduces the differences between the measured and predicted reverberation time values, showing that an accuracy within ±10% from the target reverberation time values can be achieved regardless of the absorption distribution in a room. The paper also discusses the oft neglected air absorption of sound, which may introduce considerable bias to the measurement results. The need for an air-absorption compensation procedure is highlighted, and a method for the estimation of its parameters in octave bands is proposed and compared with other approaches. The results of this study provide justification for the use of the Sabine and Eyring formulas for reverberation time predictions.

Lossless Feedback Delay Networks (FDNs) are commonly used as a design prototype for artificial reverberation algorithms. The lossless property is dependent on the feedback matrix, which connects the output of a set of delays to their inputs, and the lengths of the delays. Both, unitary and triangular feedback matrices are known to constitute lossless FDNs, however, the most general class of lossless feedback matrices has not been identified. In this contribution, it is shown that the FDN is lossless for any set of delays, if all irreducible components of the feedback matrix are diagonally similar to a unitary matrix. The necessity of the generalized class of feedback matrices is demonstrated by examples of FDN designs proposed in literature.

This paper introduces a time-variant reverberation algorithm as an extension of the feedback delay network (FDN). By modulating the feedback matrix nearly continuously over time, a complex pattern of concurrent amplitude modulations of the feedback paths evolves. Due to its complexity, the modulation produces less likely perceivable artifacts and the time-variation helps to increase the liveliness of the reverberation tail. A listening test, which has been conducted, confirms that the perceived quality of the reverberation tail can be enhanced by the feedback matrix modulation. In contrast to the prior art time-varying allpass FDNs, it is shown that unitary feedback matrix modulation is guaranteed to be stable. Analytical constraints on the pole locations of the FDN help to describe the modulation effect in depth. Further, techniques and conditions for continuous feedback matrix modulation are presented.

An established model for sound energy decay functions (EDFs) is the superposition of multiple exponentials and a noise term. This work proposes a neural-network-based approach for estimating the model parameters from EDFs. The network is trained on synthetic EDFs and evaluated on two large datasets of over 20 000 EDF measurements conducted in various acoustic environments. The evaluation shows that the proposed neural network architecture robustly estimates the model parameters from large datasets of measured EDFs while being lightweight and computationally efficient. An implementation of the proposed neural network is publicly available.

The decaying sound field in rooms is typically described by energy decay functions (EDFs). Late reverberation can deviate considerably from the ideal diffuse field, for example, in multiple connected rooms or non-uniform absorption material distributions. This paper proposes the common-slope model of late reverberation. The model describes spatial and directional late reverberation as linear combinations of exponential decays called common slopes. Its fundamental idea is that common slopes have decay times that are invariant across space and direction, while their amplitudes vary across both. We explore different approaches for determining the common slopes for large EDF sets describing different source-receiver configurations of the same environment. Among the presented approaches, the k-means clustering of decay times is the most general. Our evaluation shows that the common-slope model introduces only a small error between the modeled and the true EDF, while being considerably more compact than the traditional multi-exponential model. The amplitude variations of the common slopes yield interpretable room acoustic analyses. The common-slope model has potential applications in all fields relying on late reverberation models, such as source separation, dereverberation, echo cancellation, and parametric spatial audio rendering.