Harmonic Sinusoid Modeling of Tonal Music Events

Abstract

This thesis presents the theory, implementation and applications of the harmonic sinusoid modeling of pitched audio events. Harmonic sinusoid modeling is a parametric model that expresses an audio signal, or part of an audio signal, as the linear combination of concurrent slow-varying sinusoids, grouped together under harmonic frequency constraints. The harmonic sinusoid modeling is an extension of the sinusoid modeling, with the additional frequency constraints so that it is capable to directly model tonal sounds. This enables applications such as object-oriented audio manipulations, polyphonic transcription, instrument/singer recognition with background music, etc. The modeling system consists of an analyzer and a synthesizer. The analyzer extracts harmonic sinusoidal parameters from an audio waveform, while the synthesizer rebuilds an audio waveform from these parameters. Parameter estimation is based on a detecting-grouping-tracking framework. The detecting stage finds and estimates sinusoid atoms; the grouping stage collects concurrent atoms into harmonic groups; the tracking stage collects the atom groups at different time to form continuous harmonic sinusoid tracks. Compared to standard sinusoid model, the harmonic model focuses on harmonic groups of atoms rather than on isolated atoms, therefore naturally represents tonal sounds. The synthesizer rebuilds the audio signal by interpolating measured parameters along the found tracks. We propose the first application of the harmonic sinusoid model in digital audio editors. For audio editing, with the tonal events directly represented by a parametric model, we can implement standard audio editing functionalities on tonal events embedded in an audio signal, or invent new sound effects based on the model parameters themselves. Possibilities for other applications are suggested at the end of this thesis.