Local harmonic estimation in musical sound signals

Statistical modeling and analysis have been applied to different music-related fields, including sound synthesis and analysis. Sound can be represented as a real-valued function of time. This function can be sampled at a sufficiently small rate such that the resulting discrete version is a good approximation of the continuous version, thus enabling the study of musical sounds as a discrete time series, an entity for which many statistical techniques are available. Physical modeling suggests that many musical instruments' sounds may be characterized by a deterministic periodic and stochastic signal model. In this article the interest is in separating these two elements of the sound and finding parametric representations with musical meaning. To do so, a local harmonic model that tracks changes in pitch and in the amplitudes of the harmonics is fitted. Deterministic changes in the signal, such as pitch change, suggest that different temporal window sizes should be considered. Ways to choose appropriate window sizes are studied. Among other things, the analysis provides estimates of the harmonic signal and noise signal. Different musical composition applications may be based on these estimates.