Overview of Spectral and Physical Models for Sound, Part I

Date: 
Wed, 04/14/2010 - 4:30pm
Location: 
CCRMA Classroom [Knoll 217]
Event Type: 
DSP Seminar
Overview of Spectral and Physical Models for Sound
Part I: Daniel Bernoulli versus Jean le Rond d'Alembert (with weigh-in from Euler and Lagrange)
Julius Smith
This talk presents an overview of physical and spectral modeling approaches to sound synthesis and audio effects. Spectral modeling arguably came first, with Bernoulli's insight that the vibration of physical objects can be seen as a superposition of simple modes of vibration, each radiating sinusoidally. Later, D'Alembert introduced the wave equation for vibrating strings, together with its solution as a superposition of two traveling waves, one in each direction along the string. Since traveling waves were "obviously" not expressible as a sum of what we would now call "standing waves", a mathematical controversy was born that was to last decades. Lagrange eventually said that any mention of the vibrating-string problem made him sick in his stomach! Fortunately, the relevant mathematical questions have been resolved (Euler and Lagrange, and of course Fourier, had a lot to do with that), and we can now enjoy either approach, according to what is most appropriate for the application at hand. In this talk, I will give some examples of both types, with emphasis on developments at CCRMA over the years.
 
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