# 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)

• Arturo Camacho. Swipe: A Sawtooth Waveform Inspired Pitch Estimator for Speech and Music. PhD thesis, University of Florida, Gainesville, FL, USA, 2007.
[BibTeX▼]
• Julius O. Smith and Xavier Serra. PARSHL: An Analysis/Synthesis Program for Non-Harmonic Sounds Based on a Sinusoidal Representation. In Proceedings of the International Computer Music Conference (ICMC). Barcelona, Spain, 2005. URL: http://www.bibsonomy.org/bibtex/2fa00c44d6ff2549f4d0559a105631fd7/zazi.
[BibTeX▼]
• Alain de Cheveigné and Hideki Kawahara. YIN, a Fundamental Frequency Estimator for Speech and Music. The Journal of the Acoustical Society of America, 111(4):1917–1930, 2002.
[BibTeX▼]
• Scott Levine and Julius Smith. A Sines + Transients + Noise Audio Representation for Data Compression and Time/Pitch Scale Modifications. In Proceedings of the 105th Audio Engineering Society Convention. San Francisco, CA, 1998.
[BibTeX▼]
• Xavier Serra and Julius Smith. Spectral Modeling Synthesis: A Sound Analysis/Synthesis System Based on a Deterministic Plus Stochastic Decomposition . Computer Music Journal, 14(4):12–14, 1990.
[BibTeX▼]
• R. McAulay and T. Quatieri. Speech analysis/Synthesis based on a sinusoidal representation. Acoustics, Speech and Signal Processing, IEEE Transactions on, 34(4):744–754, 1986.
[BibTeX▼]
• T Quatieri and Rl McAulay. Speech transformations based on a sinusoidal representation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(6):1449–1464, 1986.
[BibTeX▼]

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