Towards complex matrix decomposition of spectrograms based on the relative phase offsets of harmonic sounds

In this paper we study the relative phase offsets between partials in the sustained part of harmonic sounds and investigate their suitability for complex matrix decomposition of spectrograms. We formally introduce this property in a sinusoidal model and visualise the phase relations of a musical instrument. A model of complex matrix decomposition in the time-frequency domain is derived and equations for the estimation of the model parameters are provided in the mono-phonic case. We illustrate the model with the analysis of a mono-phonic saxophone signal. The results suggest that the phase offset is able to capture inherent time-invariant phase properties of harmonic sounds and outline its potential use for complex matrix decomposition.