High-order chirplet transform for efficient reconstruction of multicomponent signals with amplitude modulated crossing ridges

Abstract

Multicomponent signals with crossing ridges, such as those encountered when measuring vocal tract resonances during singing, are challenging to analyze in time–frequency domain. The chirplet transform introduces the chirprate as a third dimension, extending the time–frequency domain to enable the separation of ridges. While existing methods assume weak amplitude modulations of signal components for the reconstruction process, a high-order chirplet transform is developed to accurately and efficiently retrieve amplitude modulation of crossing components, assuming that the instantaneous frequency of the components are already known. Analytical solving and numerical stability are obtained with a family of chirplet windows based on Hermite polynomials. The numerical results on simulated and real signals show the relevance and efficiency of the proposed method.