Devising a new filtration method and proof of self-similarity of electromyograms

The main attention is paid to the analysis of electromyogram (EMG) signals using Poincaré plots (PP). It was established that the shapes of the plots are related to the diagnoses of patients. To study the fractal dimensionality of the PP, the method of counting the coverage figures was used. The PP filtration was carried out with the help of Haar wavelets. The self-similarity of Poincaré plots for the studied electromyograms was established, and the law of scaling was used in a fairly wide range of coverage figures. Thus, the entire Poincaré plot is statistically similar to its own parts. The fractal dimensionalities of the PP of the studied electromyograms belong to the range from 1.36 to 1.48. This, as well as the values of indicators of Hurst exponent of Poincaré plots for electromyograms that exceed the critical value of 0.5, indicate the relative stability of sequences. The algorithm of the filtration method proposed in this research involves only two simple stages: Conversion of the input data matrix for the PP using the Jacobi rotation. Decimation of both columns of the resulting matrix (the so-called "lazy wavelet-transformation", or double downsampling). The algorithm is simple to program and requires less machine time than existing filters for the PP. Filtered Poincaré plots have several advantages over unfiltered ones. They do not contain extra points, allow direct visualization of short-term and long-term variability of a signal. In addition, filtered PPs retain both the shape of their prototypes and their fractal dimensionality and variability descriptors. The detected features of electromyograms of healthy patients with characteristic low-frequency signal fluctuations can be used to make clinical decisions.