| Summary: | This thesis introduces a new adaptive decomposition method - Nonlinear Mode Decomposition (NMD) - which decomposes a given signal into a set of physically meaningful oscillations within any waveform, simultaneously removing the noise. It is based on the powerful combination of two elements. First, time-frequency analysis techniques with the adaptive parameter choice make the method extremely noise-robust. Secondly, surrogate data tests are used to identify interdependent oscillations and to distinguish deterministic from random activity. The theory of linear time-frequency representations, which represent the foundation of NMD, is first reviewed and advanced, with the emphasis being placed on its practically relevant aspects. Techniques for extracting harmonic oscillations with time-varying amplitudes and frequencies from the signal’s time-frequency representation are then developed. By combining these techniques with additional procedures devised for distinguishing the retrieved oscillations from noise and for the recovery of their full waveforms, the NMD is finally formed. The performance of the method is illustrated on both simulated and real signals, and its qualitative and quantitative superiority over the other existing approaches (such as (ensemble) empirical mode decomposition, Karhunen-Loeve expansion and independent component analysis) is shown. In particular, NMD is applied for the decomposition of human blood flow signals and, based on properties of the recovered oscillations for different subject groups, certain aspects of cardiovascular ageing and (treated) hypertension are revealed. Furthermore, applications of the method for removing the measurement artifacts from a single electroencephalogram recording, and for distinguishing different kinds of systems, are also demonstrated. These examples, however, represent only a few out of many possible uses of NMD, which can be applied routinely to a diversity of signals coming from various scientific areas (geophysics, finance, life sciences etc.). The necessary MATLAB codes for running NMD are freely available for download.
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