Abstract
Among biomedical signals, repetitive or quasi-periodic signals are particularly widespread. While the periodic component is still presented these signals are characterized by period variations (fundamental frequency, amplitude, etc.). The lack of synchronization or phase shifts results in variations in similar segments’ durations, nominally identical signals demonstrate a variation at peak retention times, etc. The inverse methods of oscillation theory were proposed recently as a tool to solve the problems of modelling of repetitive signals with phase shift. In the article, the inverse method of oscillation theory is considered as a tool to solve the problems of supervised and non-supervised classification, and filtering of repetitive signals with phase shift. Examples of application are presented.
Highlights
Among biomedical signals, repetitive or quasi-periodic signals are widespread
While the periodic component is still presented in these signals they are characterized by period variations
One of the problems of the study of biological signals is the lack of synchronization or phase shifts which results in variations in similar segments’ durations, nominally identical signals demonstrate a variation at peak retention times, etc
Summary
Statistical methods of regression analysis and classification are generally based on the assumption of the presence of additive noise only which describes the distortion in amplitude alone, and are sensitive to disturbances to this assumption. The inverse methods of oscillation theory (IMOT) were proposed recently as a tool to solve the problems of modelling and of the processing of repetitive signals with phase shift. The IMOT approach is based on the assumption that observed repetitive signals can be described as a solution of a nonlinear oscillation model with perturbation which explains the distortion of both the amplitude and phase. The IMOT methods are revised as a tool to solve the problems of statistical signal processing, such as averaging, supervised and non-supervised classification, and filtering out of repetitive signals with phase shift.
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