Musical sound modeling with sinusoids plus noise

Abstract

When generating musical sound on a digital computer, it is important to have a good model whose parameters provide a rich source of meaningful sound transformations. Three basic model types are in prevalent use today for musical sound generation instrument models, spectrum models, and abstract models. Instrument models attempt to parametrize a sound at its source, such as a violin, clarinet, or vocal tract. Spectrum models attempt to parametrize a sound at the basilar membrane of the ear, discarding whatever information the ear seems to discard in the spectrum. Abstract models, such as FM, attempt to provide musically useful parameters in an abstract formula.

This article addresses the second category of synthesis techniques spectrum modeling. The main advantage of this group of techniques is the existence of analysis procedures that extract the synthesis parameters out of real sounds, thus being able to reproduce and modify actual sounds. Our particular approach is based on modeling sounds as stable sinusoids (partials) plus noise (residual component), therefore analyzing sounds with this model and generating new sounds from the analyzed data. The analysis procedure detects partials by studying the time-varying spectral characteristics of a sound and represents them with time-varying sinusoids. These partials are then subtracted from the original sound and the remaining "residual" is represented as a time-varying filtered white noise component. The synthesis procedure is a combination of additive synthesis for the sinusoidal part, and subtractive synthesis for the noise part.