# Additive & Spectral: Spectral Modeling

## McAulay/Quatieri

Sinusoidal modeling can be conisdered a higher level algorithm for the additive synthesis of harmonic sounds. It has first been used in speech processing by McAulay, R. and Quatieri (1986). For low framerates they proposed a time-domain method for partial synthesis with original phases of the partials.

R. McAulay and T. Quatieri (1986)

## SMS

The above presented sinusoidal modeling approach captures only the harmonic portion of a sound. With the Sinusoids plus Noise model (SMS), Serra and Smith (1990) introduced the Deterministic + Stochastic model for spectral modeling, in order to model components in the signal which are not captured by partial tracking. A sound is therefor modeled as a combination of a dererministic component - the sinusoids - and a stochasctic component:

$x = x_{DET} + x_{STO}$

Deterministic + Stochastic model (Serra and Smith, 1990)

## Sines + Transients + Noise

Even the harmonic and noise model can not capture all components of musical sounds. The third - and in this line last - signal component to be included are the transients.

Sines + Transients + Noise (Levine and Smith, 1998)

#### 2007

• Arturo Camacho. Swipe: A Sawtooth Waveform Inspired Pitch Estimator for Speech and Music. PhD thesis, University of Florida, Gainesville, FL, USA, 2007.
[details] [BibTeX▼]