http://hdl.handle.net/1842/3409 Thu, 23 May 2013 18:52:23 GMT 2013-05-23T18:52:23Z http://hdl.handle.net/1842/3720 Title: Percussion synthesis based on models of nonlinear shell vibration Authors: Bilbao, Stefan Abstract: The synthesis of sound based on physical models of 2-D percussion instruments is problematic and has been approached only infrequently in the literature. Beyond the computational expense inherent to the simulation of 2-D systems, a deeper difficulty is in dealing with the strong nonlinearity exhibited by thin structures when struck--this nonlinearity leads to phenomena which are not captured, even approximately, by a linear model, and nearly all synthesis work is based on the assumption that the distributed resonating component of a musical instrument is linear. Perceptually, the effects of the vibration of a thin structure at high amplitudes can be heard as crashes, pitch glides, and the slow buildup of high-frequency energy characteristic of gongs. A large family of instruments may be described, approximately, as circular thin shells, of approximately spherical geometry, in which case a tractable PDE description, described here, is available. Time-domain finite-difference schemes, in radial coordinates, are a suitable method for synthesis. Stability conditions, numerical boundary conditions both at the edge and center, and implementation details are discussed, and simulation results are presented, highlighting the various perceptual effects mentioned above. Sat, 01 May 2010 00:00:00 GMT http://hdl.handle.net/1842/3720 2010-05-01T00:00:00Z http://hdl.handle.net/1842/3718 Title: A virtual model of spring reverberation Authors: Bilbao, Stefan; Parker, Julian Abstract: The digital emulation of analog audio effects and synthesis components, through the simulation of lumped circuit components has seen a large amount of activity in recent years; electromechanical effects have seen rather less, primarily because they employ distributed mechanical components, which are not easily dealt with in a rigorous manner using typical audio processing constructs such as delay lines and digital filters. Spring reverberation is an example of such a system--a spring exhibits complex, highly dispersive behavior, including coupling between different types of wave propagation (longitudinal and transverse). Standard numerical techniques, such as finite difference schemes are a good match to such a problem, but require specialized design and analysis techniques in the context of audio processing. A model of helical spring vibration is introduced, along with a family of finite difference schemes suitable for time domain simulation. Various topics are covered, including numerical stability conditions, tuning of the scheme to the response of the model system, numerical boundary conditions and connection to an excitation and readout, implementation details, as well as computational requirements. Simulation results are presented, and full energy-based stability analysis appears in an Appendix. Sat, 01 May 2010 00:00:00 GMT http://hdl.handle.net/1842/3718 2010-05-01T00:00:00Z