Time domain analysis/resynthesis of musical tones based on polynomial interpolation techniques

Abstract

In this paper, a novel algorithm employing polynomial interpolation techniques is proposed for the analysis and resynthesis of musical tones, based on time domain information. This algorithm models a single period of oscillation as a series of features, with curves joining such features together. The trajectories of these features and the shape of the curves across the whole input signal can be parameterised, such that the signal can be analysed and resynthesised as a close approximation to the original. The current research introduced an alternative approach to analyse/resynthesise sampled musical signals in the frequency domain, one which characterises a signal by its physical structure rather than its frequency components. The results from this analysis can be used to further refine existing physical models of musical instruments.