Download Applications of Port Hamiltonian Methods to Non-Iterative Stable Simulations of the Korg35 and Moog 4-Pole Vcf This paper presents an application of the port Hamiltonian formalism to the nonlinear simulation of the OTA-based Korg35 filter circuit and the Moog 4-pole ladder filter circuit. Lyapunov analysis is
used with their state-space representations to guarantee zero-input
stability over the range of parameters consistent with the actual
circuits. A zero-input stable non-iterative discrete-time scheme
based on a discrete gradient and a change of state variables is
shown along with numerical simulations. Simulations show behavior consistent with the actual operation of the circuits, e.g.,
self-oscillation, and are found to be stable and have lower computational cost compared to iterative methods.
Download Measurement-Informed Nonlinear Modal Synthesis of 65 Classical Guitars When a classical guitar string is plucked, vibration energy flows through the bridge into the body and is radiated as sound. Synthesising this process for a large collection of instruments requires both an efficient nonlinear string model and a robust method for extracting instrument-specific parameters from measurements. This paper addresses both issues. Starting from the publicly available dataset of Mores, which provides impulse-response measurements on 65 classical guitars, modal parameters of the bridge compliance and of the bridge-to-air radiation path are extracted for each instrument. These feed a nonlinear string model in which transverse vibration is governed by a geometrically exact elastic potential coupled at an interior bridge point to the measured body data. The nonlinear potential is quadratised via the Scalar Auxiliary Variable (SAV) method, so that the equations of motion become linear in a scalar variable and a known gradient vector, even at the continuous level. After time discretisation, the coupled system is inverted through two sequential Sherman–Morrison rank-one updates (one for the bridge coupling, one for the SAV nonlinearity), yielding an O(N) algorithm per time step. Two regularisation techniques prevent long-term drift of the auxiliary variable. The complete pipeline is demonstrated by synthesising plucked notes across all frets and strings for each of the 65 guitars.
Download Simulations of Nonlinear Plate Dynamics: An Accurate and Efficient Modal Algorithm This paper presents simulations of nonlinear plate vibrations in relation to sound synthesis of gongs and cymbals. The von Kármán equations are shown and then solved in terms of the modes of the associated linear system. The modal equations obtained constitute a system of nonlinearly coupled Ordinary Differential Equations which are completely general as long as the modes of the system are known. A simple second-order time-stepping integration scheme yields an explicit resolution algorithm with a natural parallel structure. Examples are provided and the results discussed.
Download Efficient Simulation of the Bowed String in Modal Form The motion of a bowed string is a typical nonlinear phenomenon resulting from a friction force via interaction with the bow. The system can be described using suitable differential equations. Implicit numerical discretisation methods are known to yield energy consistent algorithms, essential to ensure stability of the timestepping schemes. However, reliance on iterative nonlinear root finders carries significant implementation issues. This paper explores a method recently developed which allows nonlinear systems of ordinary differential equations to be solved non-iteratively. Case studies of a mass-spring system and an ideal string coupled with a bow are investigated. Finally, a stiff string with loss is also considered. Combining semi-discretisation and a modal approach results in an algorithm yielding faster than real-time simulation of typical musical strings.
Download Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits In this work, a number of numerical schemes are presented in the
context of virtual-analog simulation. The schemes are linearlyimplicit in character, and hence directly solvable without iterative
methods. Schemes of increasing order of accuracy are constructed,
and convergence and stability conditions are proven formally. The
schemes are able to handle stiff problems very efficiently, because
of their fast update, and can be run at higher sample rates to reduce
aliasing. The cases of the diode clipper and ring modulator are
investigated in detail, including several numerical examples.
Download Bunkervik Spatial Reverb Demo This paper accompanies a demonstration of a real-time audio plug-in for a dynamic spatial reverb. The reverb is based on acoustic measurements of the Bunkervik creative arts space in Brescia, Italy. A modal synthesis reverberation engine was created based on measured impulse responses from three locations in the tunnel. Using a common set of modal frequencies the position of the receiver can be dynamically moved through the space by interpolating between data sets of residue weights and FIR filter taps. The audio plug-in also allows real-time manipulation of the high-frequency content, damping, and microphone rotation, all of which can be modulated using two LFOs.