Download Real-Time Modal Synthesis of Nonlinearly Interconnected Networks Modal methods are a long-established approach to physical modeling sound synthesis. Projecting the equation of motion of a linear, time-invariant system onto a basis of eigenfunctions yields a set of independent forced, lossy oscillators, which may be simulated efficiently and accurately by means of standard time-stepping methods. Extensions of modal techniques to nonlinear problems are possible, though often requiring the solution of densely coupled nonlinear time-dependent equations. Here, an application of recent results in numerical simulation design is employed, in which the nonlinear energy is first quadratised via a convenient auxiliary variable. The resulting equations may be updated in time explicitly, thus avoiding the need for expensive iterative solvers, dense linear system solutions, or matrix inversions. The case of a network of interconnected distributed elements is detailed, along with a real-time implementation as an audio plugin.
Download On the limits of real-time physical modelling synthesis with a modular environment One goal of physical modelling synthesis is the creation of new virtual instruments. Modular approaches, whereby a set of basic primitive elements can be connected to form a more complex instrument have a long history in audio synthesis. This paper examines such modular methods using finite difference schemes, within the constraints of real-time audio systems. Focusing on consumer hardware and the application of parallel programming techniques for CPU processors, useable combinations of 1D and 2D objects are demonstrated. These can form the basis for a modular synthesis environment that is implemented in a standard plug-in architecture such as an Audio Unit, and controllable via a MIDI keyboard. Optimisation techniques such as vectorization and multi-threading are examined in order to maximise the performance of these computationally demanding systems.
Download Large-scale Real-time Modular Physical Modeling Sound Synthesis Due to recent increases in computational power, physical modeling synthesis is now possible in real time even for relatively complex models. We present here a modular physical modeling instrument design, intended as a construction framework for string- and bar- based instruments, alongside a mechanical network allowing for arbitrary nonlinear interconnection. When multiple nonlinearities are present in a feedback setting, there are two major concerns. One is ensuring numerical stability, which can be approached using an energy-based framework. The other is coping with the computational cost associated with nonlinear solvers—standard iterative methods, such as Newton-Raphson, quickly become a computational bottleneck. Here, such iterative methods are sidestepped using an alternative energy conserving method, allowing for great reduction in computational expense or, alternatively, to real-time performance for very large-scale nonlinear physical modeling synthesis. Simulation and benchmarking results are presented.