Download Nonlinear Homogeneous Order Separation for Volterra Series Identification
This article addresses identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates nonlinear homogeneous order contributions from which Volterra kernels can be identified independently. The proposed separation method exploits phase relations between test signals rather than amplitude relations that are usually used. This method is compared with standard separation process. Its contribution to identification is illustrated on a simulated loudspeaker with nonlinear suspension.
Download Introducing Deep Machine Learning for Parameter Estimation in Physical Modelling
One of the most challenging tasks in physically-informed sound synthesis is the estimation of model parameters to produce a desired timbre. Automatic parameter estimation procedures have been developed in the past for some specific parameters or application scenarios but, up to now, no approach has been proved applicable to a wide variety of use cases. A general solution to parameters estimation problem is provided along this paper which is based on a supervised convolutional machine learning paradigm. The described approach can be classified as “end-to-end” and requires, thus, no specific knowledge of the model itself. Furthermore, parameters are learned from data generated by the model, requiring no effort in the preparation and labeling of the training dataset. To provide a qualitative and quantitative analysis of the performance, this method is applied to a patented digital waveguide pipe organ model, yielding very promising results.
Download Real-time Physical Model of a Wurlitzer and Rhodes Electronic Piano
Two well known examples of electro-acoustical keyboards played since the 60s to the present day are the Wurlitzer electric piano and the Rhodes piano. They are used in such diverse musical genres as Jazz, Funk, Fusion or Pop as well as in modern Electronic and Dance music. Due to the popularity of their unique sound and timbre, there exist various hardware and software emulations which are either based on a physical model or consist of a sample based method for sound generation. In this paper, a real-time physical model implementation of both instruments using field programmable gate array (FPGA) hardware is presented. The work presented herein is an extension of simplified models published before. Both implementations consist of a physical model of the main acoustic sound production parts as well as a model for the electromagnetic pickup system. Both models are compared to a series of measurements and show good accordance with their analog counterparts.
Download A Mechanical Mapping Model for Real-time Control of a Complex Physical Modelling Synthesis Engine with a Simple Gesture
This paper describes the design and control of a digital synthesis engine developed to imitate the sound of an acoustic wind machine, a historical theatre sound effect first designed in the nineteenth century. This work is part of an exploration of the potential of historical theatre sound effects as a resource for Sonic Interaction Design (SID). The synthesis engine is based on a physical model of friction and is programmed using the Sound Designer’s Toolkit (SDT) suite of physical modelling objects in Max/MSP. The program is controlled in real-time with a single stream of rotation data from a rotary encoder and Arduino, with complexity achieved through a mapping strategy that recreates the mechanical process at the heart of the acoustic wind machine’s sound production. The system is outlined, along with a discussion of the possible application of this approach to the modeling of other historical theatre sound effects.
Download Simulating the Friction Sounds Using a Friction-based Adhesion Theory Model
Synthesizing a friction sound of deformable objects by a computer is challenging. We propose a novel physics-based approach to synthesize friction sounds based on dynamics simulation. In this work, we calculate the elastic deformation of an object surface when the object comes in contact with other objects. The principle of our method is to divide an object surface into microrectangles. The deformation of each microrectangle is set using two assumptions: the size of a microrectangle (1) changes by contacting other object and (2) obeys a normal distribution. We consider the sound pressure distribution and its space spread, consisting of vibrations of all microrectangles, to synthesize a friction sound at an observation point. We express the global motions of an object by position based dynamics where we add an adhesion constraint. Our proposed method enables the generation of friction sounds of objects in different materials by regulating the initial value of microrectangular parameters.
Download Kinematics of Ideal String Vibration Against a Rigid Obstacle
This paper presents a kinematic time-stepping modeling approach of the ideal string vibration against a rigid obstacle. The problem is solved in a single vibration polarisation setting, where the string’s displacement is unilaterally constrained. The proposed numerically accurate approach is based on the d’Alembert formula. It is shown that in the presence of the obstacle the lossless string vibrates in two distinct vibration regimes. In the beginning of the nonlinear kinematic interaction between the vibrating string and the obstacle the string motion is aperiodic with constantly evolving spectrum. The duration of the aperiodic regime depends on the obstacle proximity, position, and geometry. During the aperiodic regime the fractional subharmonics related to the obstacle position may be generated. After relatively short-lasting aperiodic vibration the string vibration settles in the periodic regime. The main general effect of the obstacle on the string vibration manifests in the widening of the vibration spectra caused by transfer of fundamental mode energy to upper modes. The results presented in this paper can expand our understanding of timbre evolution of numerous stringed instruments, such as, the guitar, bray harp, tambura, veena, sitar, etc. The possible applications include, e.g., real-time sound synthesis of these instruments.
Download Doppler Effect of a Planar Vibrating Piston: Strong Solution, Series Expansion and Simulation
This article addresses the Doppler effect of a planar vibrating piston in a duct, as a plane wave radiation approximation generated by a loudspeaker membrane. This physical model corresponds to a nonlinear problem, because the linear propagation is excited by a moving boundary condition at the piston face: this introduces a varying propagation time between the piston and a fixed receiver. The existence of a regular function that solves the problem (a socalled “strong” solution) is proven, under a well-posed condition that guarantees that no shock occurs. This function satisfies an implicit equation to be solved. An algorithm based on the perturbation method is proposed, from which an exact solution can be built using power series. The convergence of the power series is numerically checked on several examples. Simulations derived from a truncated power series provide sound examples with audible intermodulation and distortion effects for realistic loudspeaker excursion and speed ranges.
Download Latent Force Models for Sound: Learning Modal Synthesis Parameters and Excitation Functions from Audio Recordings
Latent force models are a Bayesian learning technique that combine physical knowledge with dimensionality reduction — sets of coupled differential equations are modelled via shared dependence on a low-dimensional latent space. Analogously, modal sound synthesis is a technique that links physical knowledge about the vibration of objects to acoustic phenomena that can be observed in data. We apply latent force modelling to sinusoidal models of audio recordings, simultaneously inferring modal synthesis parameters (stiffness and damping) and the excitation or contact force required to reproduce the behaviour of the observed vibrational modes. Exposing this latent excitation function to the user constitutes a controllable synthesis method that runs in real time and enables sound morphing through interpolation of learnt parameters.
Download Energy Shaping of a Softening Duffing Oscillator Using the Formalism of Port-Hamiltonian Systems
This work takes place in the context of the development of an active control of instruments with geometrical nonlinearities. The study focuses on Chinese opera gongs that display a characteristic pitch glide in normal playing conditions. In the case of the xiaoluo gong, the fundamental mode of the instrument presents a softening behaviour (frequency glides upward when the amplitude decreases). Controlling the pitch glide requires a nonlinear model of the structure, which can be partially identified with experimental techniques that rely on the formalism of nonlinear normal modes. The fundamental nonlinear mode has been previously experimentally identified as a softening Duffing oscillator. This paper aims at performing a simulation of the control of the oscillator’s pitch glide. For this purpose, the study focuses on a single-degree-offreedom nonlinear mode described by a softening Duffing equation. This Duffing oscillator energy proves to be ill-posed - in particular, the energy becomes negative for large amplitudes of vibration, which is physically inconsistent. Then, the first step of the present study consists in redefining a new energetically well-posed model. In a second part, guaranteed-passive simulations using port-Hamiltonian formalism confirm that the new system is physically and energetically correct compared to the Duffing model. Third, the model is used for control issues in order to modify the softening or hardening behaviour of the fundamental pitch glide. Results are presented and prove the method to be relevant. Perspectives for experimental applications are finally exposed in the last section of the paper.
Download On Iterative Solutions for Numerical Collision Models
Nonlinear interactions between different parts of musical instruments present several challenges regarding the formulation of reliable and efficient numerical sound synthesis models. This paper focuses on a numerical collision model that incorporates impact damping. The proposed energy-based approach involves an iterative solver for the solution of the nonlinear system equations. In order to ensure the efficiency of the presented algorithm a bound is derived for the maximum number of iterations required for convergence. Numerical results demonstrate energy conservation as well as convergence within a small number of iterations, which is usually much lower than the predicted bound. Finally, an application to music acoustics, involving a clarinet simulation, shows that including a loss mechanism during collisions may have a significant effect on sound production.