Inter-component phase processing of quasipolyharmonic signals

•Generalized research in the field of inter-component phase signal processing.•Defined a notion and properties of inter-component phase relations (ICPR) estimates.•ICPR quantify relative delays occurred between components during signal propagation.•Discussed why higher-order spectra may not reveal the non-linear nature of speech.•Demonstrated potential of shaft misalignment monitoring using ICPR statistics. The paper presents a generalization of theoretical and experimental research in the field of inter-component phase signal processing based on instantaneous phase estimates of multiple or rational frequency harmonic components. We propose to model harmonic phase of each component of quasipolyharmonic signal with consideration of relative delays that occur on different frequencies during the signal propagation. Based on the proposed harmonic phase model, it is argued the inter-component phase relations carry the information about parameters of these relative delays. We introduce the general expression for the inter-component phase relations estimates, showing their temporal constancy and invariance to the time–frequency shifts and fluctuations of the harmonic amplitudes. These properties correspond to the findings obtained for signal propagation experiments with prior knowledge of harmonic phases. Applicability of proposed estimates for processing of natural signals is justified by results of past speech processing research (including speaker identification and speech enhancement) and novel experiments on condition monitoring of industrial machines. By employing the proposed harmonic phase model, we discuss why the earlier research on speech structure using higher-order spectra techniques did not reveal the non-linear nature of speech. We carry out simple experiments on condition monitoring of industrial machines to demonstrate the potential of distinguishing between different configurations of shaft misalignment based on the distribution of standard deviation of inter-component phase relations.