Damping Density of an Absorptive Shoebox Room Derived from the Image-Source Method

The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary absorption. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. In this paper, we derive a closed-form expression for the damping density, which characterizes the overall multi-slope energy decay. The omnidirectional energy decay over time is directly derived from the damping density. The resulting energy decay model accurately matches the late reverberation simulated via the image-source method. The proposed model allows the fast stochastic synthesis of late reverberation by shaping noise with the energy envelope. Simulations of various wall damping coefficients demonstrate the model's accuracy. The proposed model consistently outperforms the energy decay prediction accuracy compared to a state-of-the-art approximation method. The paper elaborates on the proposed damping density's applicability to modeling multi-sloped sound energy decay, predicting reverberation time in non-diffuse sound fields, and fast frequency-dependent RIR synthesis.

Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.