A sound decomposition system based on a deterministic plus residual model

Abstract

Based on a deterministic plus residual model, a system is developed that extracts stable sinusoidal components from a musical sound and leaves a residual waveform as a result. The two components can be added to obtain an identity with the original sound. The technique is based on the short-time Fourier transform. From the set of spectra returned by the transform, the prominent peaks are detected at every frame and assigned to a number of frequency trajectories by means of a peak continuation algorithm. The relevance of this algorithm is that it detects the stable sinusoids present in the original sound (the deterministic component). Each trajectory includes an amplitude, frequency, and phase value for every analysis frame. From each trajectory, a time varying sinusoid is generated and the sum of all these sinusoids form the deterministic component. Since the synthesized waveform has preserved amplitude and phase of the original sound, a time domain subtraction succeeds in obtaining a residual waveform free of the detected sinusoidal components.