At present, spectacular progress is achieved in the development of probabilistic approach to the basic principles of quantum mechanics (for instance, see [1]). This approach is based on tomographic representation of density matrix and the Wigner function [2,3], yielded by the Radon transform [4]. The probabilistic approach made it possible to apply the methods of quantum mechanics in description of various signals. The most comprehensive description of this method is given in [5]. Especially interesting are the attempts to use the tomographic approach to transform and analyze the medical signals [6,7]. When processing such signals, the Fourier transform is widely used, representing the signal as a function of the frequency ω. This transform is currently a common tool in the analysis of Electrocardiograms (ECGs). The tomographic transformation makes it possible to represent the signal as a positively defined function that simultaneously depends on both time and frequency. Recently, the tomographic representation was applied for processing some biological signals [8,9]. These studies were carried out to evaluate new perspectives that open up when analyzing a human ECG using tomographic representation.
Tomographic Representation
The tomographic representation can be introduced as a generalization of the Wigner function to a positive definite distribution [10]. A rigorous description of this mathematical transformation is given in [5], and a detailed description of its application to the analysis of some biological signals is given in [8,9]. Here we will give a brief description of the essence of the tomographic representation.
Read More About This Article: 10.31031/OABB.2024.03.000568
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