Download Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman Based Deep Learning Methods This paper presents an examination of State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Through experiments with datasets generated under different initial conditions and sample rates, we assess the capacity of these models to accurately model the complex behaviours observed in string dynamics. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in nonlinear cases for long-sequence modelling. We inform the design of these architectures with the structure of the problems at hand. Although challenges remain in extending model predictions beyond the training horizon (i.e., extrapolation), the focus of our investigation lies in the models’ ability to generalise across different initial conditions within the training time interval. This research contributes insights into the physical modelling of dynamical systems (in particular those addressing musical acoustics) by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement. Our results highlight the efficacy of these models in simulating non-linear dynamics and emphasise their wide-ranging applicability in accurately modelling dynamical systems over extended sequences.
Download Quadratic Spline Approximation of the Contact Potential for Real-Time Simulation of Lumped Collisions in Musical Instruments Collisions are an integral part of the sound production mechanism in a wide variety of musical instruments. In physics-based realtime simulation of such nonlinear phenomena, challenges centred around efficient and accurate root-finding arise. Nonlinearly implicit schemes are normally ill-suited for real-time simulation as they rely on iterative solvers for root-solving. Explicit schemes overcome this issue at the cost of a slightly larger error for a given sample rate. In this paper, for the case of lumped collisions, an alternate approach is proposed by approximating the contact potential curve. The approximation is described, and is shown to lead to a non-iterative update for an energy-stable nonlinearly implicit scheme. The method is first tested on single mass-barrier collision simulations, and then employed in conjunction with a modal string model to simulate hammer-string and slide-string interaction. Results are discussed in comparison with existing approaches, and real-time feasibility is demonstrated.
Download Real-Time Guitar Synthesis The synthesis of guitar tones was one of the first uses of physical modeling synthesis, and many approaches (notably digital waveguides) have been employed. The dynamics of the string under playing conditions is complex, and includes nonlinearities, both inherent to the string itself, and due to various collisions with the fretboard, frets and a stopping finger. All lead to important perceptual effects, including pitch glides, rattling against frets, and the ability to play on the harmonics. Numerical simulation of these simultaneous strong nonlinearities is challenging, but recent advances in algorithm design due to invariant energy quadratisation and scalar auxiliary variable methods allow for very efficient and provably numerically stable simulation. A new design is presented here that does not employ costly iterative methods such as the Newton-Raphson method, and for which required linear system solutions are small. As such, this method is suitable for real-time implementation. Simulation and timing results are presented.
Download A Highly Parametrized Scattering Delay Network Implementation for Interactive Room Auralization Scattering Delay Networks (SDNs) are an interesting approach to artificial reverberation, with parameters tied to the room’s physical properties and the computational efficiency of delay networks. This paper presents a highly-parametrized and real-time plugin of an SDN. The SDN plugin allows for interactive room auralization, enabling users to modify the parameters affecting the reverberation in real-time. These parameters include source and receiver positions, room shape and size, and wall absorption properties. This makes our plugin suitable for applications that require realtime and interactive spatial audio rendering, such as virtual or augmented reality frameworks and video games. Additionally, the main contributions of this work include a filter design method for wall sound absorption, as well as plugin features such as air absorption modeling, various output formats (mono, stereo, binaural, and first to fifth order Ambisonics), open sound control (OSC) for controlling source and receiver parameters, and a graphical user interface (GUI). Evaluation tests showed that the reverberation time and the filter design approach are consistent with both theoretical references and real-world measurements. Finally, performance analysis indicated that the SDN plugin requires minimal computational resources.
Download A Common-Slopes Late Reverberation Model Based on Acoustic Radiance Transfer In rooms with complex geometry and uneven distribution of energy losses, late reverberation depends on the positions of sound sources and listeners. More precisely, the decay of energy is characterised by a sum of exponential curves with position-dependent amplitudes and position-independent decay rates (hence the name common slopes). The amplitude of different energy decay components is a particularly important perceptual aspect that requires efficient modeling in applications such as virtual reality and video games. Acoustic Radiance Transfer (ART) is a room acoustics model focused on late reverberation, which uses a pre-computed acoustic transfer matrix based on the room geometry and materials, and allows interactive changes to source and listener positions. In this work, we present an efficient common-slopes approximation of the ART model. Our technique extracts common slopes from ART using modal decomposition, retaining only the non-oscillating energy modes. Leveraging the structure of ART, changes to the positions of sound sources and listeners only require minimal processing. Experimental results show that even very few slopes are sufficient to capture the positional dependency of late reverberation, reducing model complexity substantially.
Download Wave Digital Model of the MXR Phase 90 Based on a Time-Varying Resistor Approximation of JFET Elements Virtual Analog (VA) modeling is the practice of digitally emulating analog audio gear. Over the past few years, with the purpose of recreating the alleged distinctive sound of audio equipment and musicians, many different guitar pedals have been emulated by means of the VA paradigm but little attention has been given to phasers. Phasers process the spectrum of the input signal with time-varying notches by means of shifting stages typically realized with a network of transistors, whose nonlinear equations are, in general, demanding to be solved. In this paper, we take as a reference the famous MXR Phase 90 guitar pedal, and we propose an efficient time-varying model of its Junction Field-Effect Transistors (JFETs) based on a channel resistance approximation. We then employ such a model in the Wave Digital domain to emulate in real-time the guitar pedal, obtaining an implementation characterized by low computational cost and good accuracy.
Download Modified Late Reverberation in an Audio Augmented Reality Scenario This paper presents a headphone-based audio augmented reality demonstrator showcasing the effects of manipulated late reverberation in rendering virtual sound sources. The setup is based on a dataset of binaural room impulse responses measured along a 2 m long line, which is used to imitate the reproduction of a pair of loudspeakers. Therefore, listeners can explore the virtual sources by moving back and forth and rotating arbitrarily on this line. The demo allows the user to adjust the late reverberation tail of the auralizations interactively from shorter to longer decay times regarding the baseline decay behavior. Modification of the decay times is based on resynthesizing the late reverberation using frequencydependent shaping of binaural white noise and modal reconstruction. The paper includes descriptions of the frameworks used for this demo and an overview of the required data and processing steps.
Download Differentiable Active Acoustics - Optimizing Stability via Gradient Descent Active acoustics (AA) refers to an electroacoustic system that actively modifies the acoustics of a room. For common use cases, the number of transducers—loudspeakers and microphones—involved in the system is large, resulting in a large number of system parameters. To optimally blend the response of the system into the natural acoustics of the room, the parameters require careful tuning, which is a time-consuming process performed by an expert. In this paper, we present a differentiable AA framework, which allows multi-objective optimization without impairing architecture flexibility. The system is implemented in PyTorch to be easily translated into a machine-learning pipeline, thus automating the tuning process. The objective of the pipeline is to optimize the digital signal processor (DSP) component to evenly distribute the energy in the feedback loop across frequencies. We investigate the effectiveness of DSPs composed of finite impulse response filters, which are unconstrained during the optimization. We study the effect of multiple filter orders, number of transducers, and loss functions on the performance. Different loss functions behave similarly for systems with few transducers and low-order filters. Increasing the number of transducers and the order of the filters improves results and accentuates the difference in the performance of the loss functions.
Download Revisiting the Second-Order Accurate Non-Iterative Discretization Scheme In the field of virtual analog modeling, a variety of methods have been proposed to systematically derive simulation models from circuit schematics. However, they typically rely on implicit numerical methods to transform the differential equations governing the circuit to difference equations suitable for simulation. For circuits with non-linear elements, this usually means that a non-linear equation has to be solved at run-time at high computational cost. As an alternative to fully-implicit numerical methods, a family of non-iterative discretization schemes has recently been proposed, allowing a significant reduction of the computational load. However, in the original presentation, several assumptions are made regarding the structure of the ODE, limiting the generality of these schemes. Here, we show that for the second-order accurate variant in particular, the method is applicable to general ODEs. Furthermore, we point out an interesting connection to the implicit midpoint method.
Download Evaluating Neural Networks Architectures for Spring Reverb Modelling Reverberation is a key element in spatial audio perception, historically achieved with the use of analogue devices, such as plate and spring reverb, and in the last decades with digital signal processing techniques that have allowed different approaches for Virtual Analogue Modelling (VAM). The electromechanical functioning of the spring reverb makes it a nonlinear system that is difficult to fully emulate in the digital domain with white-box modelling techniques. In this study, we compare five different neural network architectures, including convolutional and recurrent models, to assess their effectiveness in replicating the characteristics of this audio effect. The evaluation is conducted on two datasets at sampling rates of 16 kHz and 48 kHz. This paper specifically focuses on neural audio architectures that offer parametric control, aiming to advance the boundaries of current black-box modelling techniques in the domain of spring reverberation.