Sines + Noise Modeling

As mentioned in the introduction to this chapter, it takes many sinusoidal components to synthesize noise well (as many as 25 per critical band of hearing under certain conditions [82]). When spectral peaks are that dense, they are no longer perceived individually, and it suffices to match only their statistics to a perceptually equivalent degree.

Sines+Noise Synthesis generalizes the sinusoidal signal models to include a filtered noise component, as depicted in Fig.9.12.

The time-varying spectrum of the signal is assumed to be made up of a deterministic component (the sinusoids) and a stochastic component (time-varying filtered noise):

where and are the instantaneous amplitude and phase of the th sinusoidal component, and is the residual, or noise signal, assumed to be well modeled by filtered white noise:

where is the white noise, and is the impulse response of a time varying linear filter. Specifically, is the response at time to an impulse at time .

Note that filtered white noise is what is generally known in computer music as subtractive synthesis [175]. Thus, the best additive synthesis involves some subtractive synthesis as well.

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Subsections

• Sines+Noise Analysis Procedure

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.