Improving the Estimation of Trajectories of Partials by the Use of the Ambiguity Function for Additive Synthesis

Diploma thesis 1900KB

The Additive Analysis/Synthesis model represents sounds as the superposition of sinusoidal components with time-evolving parameters. Crucial parts of this technique are, among others, the estimation of the parameters (instantaneous frequency and amplitude and the initial phase of a single partial tone at a given time) and the tracking of the temporal evolution of corresponding partials by means of these parameters.

In this thesis we use the Ambiguity Function (a member of the family of bilinear timefrequency distributions) for the estimation of frequency and amplitude. The initial phase is calculated from the Analytic Signal. Finally, we show how a Hidden Markov Model can be used for the tracking of partials. In addition to the aforementioned parameters, the Ambiguity Function provides us with an estimator for the chirp rate, which can be used to improve the tracking of partials.

A prototype application developed for this thesis using MATLAB shows an improvement of the estimators and the assignment of partials to trajectories compared to more traditional methods.