A real-time simulation of physical models of musical instruments has applications in a variety of situations where a proposed physical change needs to be instantly auralized. The compactness and computational power of Field Programmable Gate Arrays make it possible to implement Finite Difference methods in the simulation. These methods are based on a discrete representation in both the spatial and time domains of the partial differential equations that represent the physical behavior of the instrument. However unlike large computer simulations, the real-time requirement necessitates special ways of representing the simulation. The authors illustrate this approach using a string-excitation model of a North American five-string banjo, which includes five strings, a membrane, and air cavity. Three examples show how real-time models can be used by musicians in a live-music setting, researchers exploring instrument acoustics, and instrument builders in the process of making design decisions.
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