On comparison of phase alignments of harmonic components
This paper provides a method for comparing phase angles of harmonic sound sources. In particular, we propose an algorithm for decomposing the difference between two sets of phases into a harmonic part, which represents the phase progress of harmonic components, and a residue part, which represents all causes of deviations from perfect harmonicity. This decomposition allows us to compare phase alignments regardless of an arbitrary time shift, and handle harmonic and noise/inharmonic parts of the phase angle separately to improve existing algorithms that handles harmonic sound sources using phase measurements. These benefits are demonstrated with a new phase-based pitch marking algorithm and an improved time-scale and pitch modification scheme using traditional harmonic sinusoidal modelling.