Sinusoidal Modeling

Definition

Audio analysis/synthesis technique (McAulay {AMP} Quatieri, 1986) representing sound as a sum of time-varying sinusoids, each described by magnitude, frequency, and phase tracks. Enables high-quality time-scale and pitch modification, and forms the basis for harmonic-percussive separation.

Key Ideas

• Analysis: track spectral peaks across frames, linking them into sinusoidal trajectories.
• Synthesis: sum the sinusoidal components, add residual (noise) component for completeness.
• Sinusoids+Noise model: deterministic (sinusoidal) + stochastic (noise) decomposition.
• Harmonic-percussive separation: harmonic components = stable sinusoidal tracks; percussive = transient noise bursts.
• Foundation for many pre-deep-learning separation and modification systems.

Relationships

• Contrast with spectrogram-based representations (../concepts/spectrogram-unets)
• Related to ../concepts/non-negative-matrix-factorization-audio — both decompose audio, different bases
• Modern relevance: hybrid systems combining sinusoidal modeling + neural residual processing

Sources

None ingested yet — seed batch setup.