Physical Modeling Synthesis

Physical models used in music sound synthesis are generally one of two basic types: lumped and distributed. Lumped models consist, in principle, of masses, springs, dampers, and nonlinear elements, and they can be used to approximate physical systems such as a brass player's lips, a singer's vocal folds, or a piano hammer.

When a mass and spring are connected, an elementary second-order resonator is formed. In digital audio signal processing, a second-order resonator is implemented using a two-pole digital filter. As a result, lumped models are typically implemented using second-order digital filters as building blocks.

On the other hand, distributed model implementations typically consist of delay lines (often called ``digital waveguides'' when used for physical modeling), in combination with digital filters and nonlinear elements. They model wave propagation in distributed media such as strings, bores, horns, plates, and acoustic spaces. In digital waveguide models, distributed losses and dispersion are still summarized and lumped at discrete points as digital filters, separating out the pure delay-line which represents ideal propagation delay. Distributed waveguide models can be freely combined with lumped filter models; for example, a brass instrument model typically consists of a lumped model for the ``lip reed'' and a distributed waveguide model for the horn.