TitleStatistics and Music: Fitting a Local Harmonic Model to Musical Sound Signals
Publication TypeThesis
Year of Publication1998
AuthorsIrizarry, R
AdvisorBrillinger, D
Academic DepartmentStatistics
Number of Pages137
UniversityUC Berkeley
CityBerkeley, CA

Statistical modeling and analysis have been applied to different music related fields. One of them is sound synthesis and analysis. Sound can be represented as a real-valued function of time. This function can be sampled at a small enough rate so that the resulting discrete version is almost as good as the continuous one. This permits one to study musical sounds as a discrete time series, an entity for which many statistical techniques are available. Physical modeling suggests that many musical instruments’ sounds are characterized by a harmonic and an additive noise signal. The noise is not something to get rid of rather it’s an important part of the signal. In this research the interest is in separating these two elements of the sound. To do so, a local harmonic model that tracks changes in pitch and of the amplitude of the harmonics is fit. Deterministic changes in the signal, such as pitch change, suggest that different temporal window sizes should be considered. Various ways to choose appropriate window sizes are studied. Amongst other things our analysis provides estimates of the harmonic signal and of the noise signal. Different musical composition applications may be based on the estimates.