Sinusoid Modeling in a Harmonic Context
This article discusses harmonic sinusoid modeling. Unlike standard sinusoid analyzers, the harmonic sinusoid analyzer keeps close watch on partial harmony from an early stage of modeling, therefore guarantees the harmonic relationship among the sinusoids. The key element in harmonic sinusoid modeling is the harmonic sinusoid particle, which can be found by grouping short-time sinusoids. Instead of tracking short-time sinusoids, the harmonic tracker operates on harmonic particles directly. To express harmonic partial frequencies in a compact and robust form, we have developed an inequality-based representation with adjustable tolerance on frequency errors and inharmonicity, which is used in both the grouping and tracking stages. Frequency and amplitude continuity criteria are considered for tracking purpose. Numerical simulations are performed on simple synthesized signals.