Fade-in Reverberation in Multi-room Environments Using the Common-Slope Model

TL;DR

The paper addresses fade-in reverberation in multi-room environments where line-of-sight between source and receiver is absent. It extends the common-slope model by fitting octave-band envelopes $s_b(\mathbf{x},t)$ as a linear combination of decaying exponentials with shared times $T_{b,k}$ and by permitting negative amplitudes $\hat{A}_{b,k,\mathbf{x}}$ while removing the direct sound term from the fit, all evaluated across 7 octave bands. Amplitudes $\hat{A}_{b,k,\mathbf{x}}$, a noise term $\hat{N}_{b,\mathbf{x}}$, and decay times $T_{b,k}$ are estimated via nonlinear least squares with a positivity constraint on the envelope after removing the noise component; decay times are prederived using K-means clustering. Experiments on simulated and real multi-room data show that FADE-IN captures fade-in reverberation that the original positive-only model could not, enabling more realistic synthesis and analysis of coupled-room acoustics with potential AR/VR applications.

Abstract

In multi-room environments, modelling the sound propagation is complex due to the coupling of rooms and diverse source-receiver positions. A common scenario is when the source and the receiver are in different rooms without a clear line of sight. For such source-receiver configurations, an initial increase in energy is observed, referred to as the "fade-in" of reverberation. Based on recent work of representing inhomogeneous and anisotropic reverberation with common decay times, this work proposes an extended parametric model that enables the modelling of the fade-in phenomenon. The method performs fitting on the envelopes, instead of energy decay functions, and allows negative amplitudes of decaying exponentials. We evaluate the method on simulated and measured multi-room environments, where we show that the proposed approach can now model the fade-ins that were unrealisable with the previous method.

Figures (8)

• Figure 1: A coupled room example with three rooms from the simulation dataset. The "$\times$" indicates the source position and the three stars, $\bigstar$, show the receiver positions.
• Figure 2: An example of how the FADE-IN and POS-ONLY model performs on RIRs with fade-in reverberation. Here, the result of the frequency band centered at 2000 Hz is shown. Note the fitting result on the initial part of RIRs. While the FADE-IN model can capture the fade-in behavior, the POS-ONLY model cannot.
• Figure 3: The FADE-IN model result on the simulation dataset, summarizing the results in the 500 Hz, 1 kHz, and 2 kHz octave bands. The source location is marked with the green "$\times$" and the receivers are distributed uniformly across the rooms. The amplitudes of each decay time at all receiver positions are shown. The spatial distribution of negative amplitudes can be observed.
• Figure 4: RMSE of model fitted envelopes and the original RIR envelopes at all receiver locations are shown. The source location is marked with "$\times$". Plotted values are the sum of RMSE over all 7 octave bands. The top figure shows the result of the FADE-IN model and the bottom shows that of the POS-ONLY model. Especially in R3, it can be seen that the FADE-IN model fits better than the POS-ONLY model.
• Figure 5: Map of the real-world dataset. The measurement trajectory and locations are marked with a line and circles, respectively. The locations of the loudspeakers are labeled from L1 to L4. The trajectory starts in front of L1 and a total of 77 measurements were made along the trajectory.