Complex discrete samples in electrocardiosignal processing tasks
Authors: Bulgakov Yu.A. , Vityazeva T.A. , Mikheev A.A. 
Published: November 2021

A typical task of preprocessing an electrocardiosignal is to eliminate the isoline drift. The presence of the isoline drift changes the position of the ST segment relative to the zero line, which leads to a distortion of the informative parameters of the ST segment. Modern electrocardiographs are equipped with high-pass filters for isoline drift removal. In this case, along with the isoline drift, a part of the spectral components of the useful signal is removed from the electrocardiogram signal. Preservation of the components of the spectrum of the electrocardiogram signal is possible by interpolating discrete samples of the isoline drift signal taken on the PQ segment or the TP interval. In this case, the sampling rate of the isoline drift signal is determined by the heart rate. Consequently, when the frequency of the isoline drift signal changing increases, the accuracy of its recovery deteriorates, and when half of the heart rate is reached, recovery becomes impossible. Purpose – the working purpose is to find ways to eliminate the isoline drift even in the presence of components in its spectrum with frequencies reaching the heart rate, while preserving the informative spectral components of the electrocardiosignal. This purpose can be achieved by converting the samples of the isoline drift signal taken at the TP interval of the electrocardiosignal into a group of samples forming a complex discrete sample (CDS). In the spectrum of the CDS sequence, the specified spectral zones can be suppressed. It is sufficient to suppress the first spectral zone at the sampling rate equal to the average heart rate to isolate the isoline drift. In this case, the frequency of the isolated isoline drift signal can theoretically be increased to the sampling rate, which is up to the heart rate. Due to the heart rate variability, the isoline drift signal samples taken at the TP interval will have a varying repetition period (sampling period). To take this fact into account, the following tasks have been solved. The analysis of the spectral composition of the sequences of samples, from which complex discrete samples are formed, has been carried out with a changing sampling rate. Pulse-frequency modulation is used as a mathematical model of the sample sequence. It has been found that with a changing sampling rate, the side components remain non-suppressed in the suppressed spectral zone at the frequencies that differ from the sampling rate by the frequency of sampling rate change. The conditions for the equality of all spectral components in the suppressed spectral zone to zero have been determined. Mathematical expressions that describe these conditions and allow us to determine the amplitude-time parameters of the CDS necessary for the implementation of these conditions have been obtained. Mathematical simulation of the CDS spectra, which confirmed the workability of the proposed description of the CDS with a changing sampling period, has been carried out. The obtained mathematical expressions allow us to determine the structure and amplitude-time parameters of complex discrete samples that provide suppression of the specified spectral components with a changing sampling period, which provides an extension of the frequency range of the isolated isoline drift signal while preserving the informative components of the electrocardiosignal.