The reverberation time is one of the most prominent acoustical qualities of a physical room. Therefore, it is crucial that artificial reverberation algorithms match a specified target reverberation time accurately. In feedback delay networks, a popular framework for modeling room acoustics, the reverberation time is determined by combining delay and attenuation filters such that the frequencydependent attenuation response is proportional to the delay length and by this complying to a global attenuation-per-second. However, only few details are available on the attenuation filter design as the approximation errors of the filter design are often regarded negligible. In this work, we demonstrate that the error of the filter approximation propagates in a non-linear fashion to the resulting reverberation time possibly causing large deviation from the specified target. For the special case of a proportional graphic equalizer, we propose a non-linear least squares solution and demonstrate the improved accuracy with a Monte Carlo simulation.

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Decorrelation of audio signals is a critical step for spatial sound reproduction on multichannel configurations. Correlated signals yield a focused phantom source between the reproduction loudspeakers and may produce undesirable comb-filtering artifacts when the signal reaches the listener with small phase differences. Decorrelation techniques reduce such artifacts and extend the spatial auditory image by randomizing the phase of a signal while minimizing the spectral coloration. This paper proposes a method to optimize the decorrelation properties of a sparse noise sequence, called velvet noise, to generate short sparse FIR decorrelation filters. The sparsity allows a highly efficient time-domain convolution. The listening test results demonstrate that the proposed optimization method can yield effective and colorless decorrelation filters. In comparison to a white noise sequence, the filters obtained using the proposed method preserve better the spectrum of a signal and produce good quality broadband decorrelation while using 76% fewer operations for the convolution. Satisfactory results can be achieved with an even lower impulse density which decreases the computational cost by 88%.

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Artificial reverberation algorithms generally imitate the frequency-dependent decay of sound in a room quite inaccurately. Previous research suggests that a 5% error in the reverberation time (T60) can be audible. In this work, we propose to use an accurate graphic equalizer as the attenuation filter in a Feedback Delay Network reverberator. We use a modified octave graphic equalizer with a cascade structure and insert a high-shelf filter to control the gain at the high end of the audio range. One such equalizer is placed at the end of each delay line of the Feedback Delay Network. The gains of the equalizer are optimized using a new weighting function that acknowledges nonlinear error propagation from filter magnitude response to reverberation time values. Our experiments show that in real-world cases, the target T60 curve can be reproduced in a perceptually accurate manner at standard octave center frequencies. However, for an extreme test case in which the T60 varies dramatically between neighboring octave bands, the error still exceeds the limit of the just noticeable difference but is smaller than that obtained with previous methods. This work leads to more realistic artificial reverberation.

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Physical accuracy of virtual acoustics receives increasing attention due to renewed interest in virtual and augmented reality applications. So far, the modeling of vibrating objects as point sources is a common simplification which neglects effects caused by their spatial extent. In this contribution, we propose a technique for the interconnection of a distributed source to a room model, based on a modal representation of source and room. In particular, we derive a connection matrix that describes the coupling between the modes of the source and the room modes in an analytical form. Therefore, we consider the example of a string that is oscillating in a room. Both, room and string rely on well established physical descriptions that are modeled in terms of transfer functions. The derived connection of string and room defines the coupling between the characteristic string and room modes. The proposed structure is analyzed by numerical evaluations and sound examples on the supplementary website.

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Feedback delay networks (FDNs) are recursive filters, which are widely used for artificial reverberation and decorrelation. While there exists a vast literature on a wide variety of reverb topologies, this work aims to provide a unifying framework to design and analyze delay-based reverberators. To this end, we present the Feedback Delay Network Toolbox (FDNTB), a collection of the MATLAB functions and example scripts. The FDNTB includes various representations of FDNs and corresponding translation functions. Further, it provides a selection of special feedback matrices, topologies, and attenuation filters. In particular, more advanced algorithms such as modal decomposition, time-varying matrices, and filter feedback matrices are readily accessible. Furthermore, our toolbox contains several additional FDN designs. Providing MATLAB code under a GNU-GPL 3.0 license and including illustrative examples, we aim to foster research and education in the field of audio processing.

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Artificial reverberation is an audio effect used to simulate the acoustics of a space while controlling its aesthetics, particularly on sounds recorded in a dry studio environment. Delay-based methods are a family of artificial reverberators using recirculating delay lines to create this effect. The feedback delay network is a popular delay-based reverberator providing a comprehensive framework for parametric reverberation by formalizing the recirculation of a set of interconnected delay lines. However, one known limitation of this algorithm is the initial slow build-up of echoes, which can sound unrealistic, and overcoming this problem often requires adding more delay lines to the network. In this paper, we study the effect of adding velvet-noise filters, which have random sparse coefficients, at the input and output branches of the reverberator. The goal is to increase the echo density while minimizing the spectral coloration. We compare different variations of velvet-noise filtering and show their benefits. We demonstrate that with velvet noise, the echo density of a conventional feedback delay network can be exceeded using half the number of delay lines and saving over 50% of computing operations in a practical configuration using low-order attenuation filters.

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In virtual acoustics, it is common to simulate the early part of a Room Impulse Response using approaches from geometrical acoustics and the late part using Feedback Delay Networks (FDNs). In order to transition from the early to the late part, it is useful to slowly fade-in the FDN response. We propose two methods to control the fade-in, one based on double decays and the other based on modal beating. We use modal analysis to explain the two concepts for incorporating this fade-in behaviour entirely within the IIR structure of a multiple input multiple output FDN. We present design equations, which allow for placing the fade-in time at an arbitrary point within its derived limit.

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A filtering algorithm for generating subtle random variations in sampled sounds is proposed. Using only one recording for impact sound effects or drum machine sounds results in unrealistic repetitiveness during consecutive playback. This paper studies spectral variations in repeated knocking sounds and in three drum sounds: a hihat, a snare, and a tomtom. The proposed method uses a short pseudo-random velvet-noise filter and a low-shelf filter to produce timbral variations targeted at appropriate spectral regions, yielding potentially an endless number of new realistic versions of a single percussive sampled sound. The realism of the resulting processed sounds is studied in a listening test. The results show that the sound quality obtained with the proposed algorithm is at least as good as that of a previous method while using 77% fewer computational operations. The algorithm is widely applicable to computer-generated music and game audio.

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A perceptual study revealing a novel connection between modal properties of feedback delay networks (FDNs) and colorless reverberation is presented. The coloration of the reverberation tail is quantified by the modal excitation distribution derived from the modal decomposition of the FDN. A homogeneously decaying allpass FDN is designed to be colorless such that the corresponding narrow modal excitation distribution leads to a high perceived modal density. Synthetic modal excitation distributions are generated to match modal excitations of FDNs. Three listening tests were conducted to demonstrate the correlation between the modal excitation distribution and the perceived degree of coloration. A fourth test shows a significant reduction of coloration by the colorless FDN compared to other FDN designs. The novel connection of modal excitation, allpass FDNs, and perceived coloration presents a beneficial design criterion for colorless artificial reverberation.

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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.

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