Computational implementation of the Cascade Hilbert-Zero Decomposition and perspectives of its applications for biophysical signal processing
Eugene B. Postnikov, 1 Elena A. Lebedeva, 2 Andrey Yu. Zyubin, 3 Anastasia I. Lavrova 3,4 1 Kursk State University, Russia 2 Saint-Petersburg State University Russia, 3 Immanuel Kant Baltic Federal University, Russia 4 Saint-Petersburg State Research Institute of Phthisiopulmonology, Russia
Abstract
We propose a novel method for processing data with serial localized peaks intended to distinguish between individual components even when they form a mono-modal but complicatedly shaped structure. The essence of the method consists of a cascade of local non-linear approximations by the Gaussian function of the vicinity of the zero-crossings of the signal’s Hilbert transform. At the first level, this procedure is applied to the processed signal directly; at the next level, it is applied to residuals between the signal and approximations on the previous levels. As a practical example, we consider the decomposition of Raman spectra recorded from different strains of Mycobacterium tuberculosis into the set of lines corresponding to different molecular components. Finally, we discuss other areas of applicability for the proposed method of signal processing.
Speaker
Eugene B. Postnikov
Kursk State University
Russia
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