Calculating Singular Integrals with Cauchy Kernels in Digital Processing of Gastroenterological Medical Signals

This article within the framework of the research work is devoted to the study of the problem of integrals. Singular integrals are usually encountered in the deep analysis of biomedical signals, which are characterized by sharp changes in continuity and discontinuity. Efficient and accurate evaluation of this type of integral is of great importance in the diagnostic process, especially in spectral analysis and identification of specific signals in gastrointestinal diseases. In this article, I have extensively discussed the mathematical foundations of the use of Cauchy kernels for the approximate calculation of singular integrals and their algorithmic methods. In this regard, modern methods are proposed to further improve the accuracy of signal detection, noise suppression and accuracy in the diagnostic process, since the complexity of gastrointestinal signals and the negative impact of noise and interference on performance are also considered in this study. The proposed method simplifies the interpretation of complex signals, increases the accuracy of spectral analysis results, and automates medical procedures. These methods, in addition to increasing diagnostic accuracy, create new ways to correctly assess the patient's condition using medical markers. The relevance of the research to the development of algorithmic solutions adapted to data processing and biomedical interpretation processes increases its relevance. Therefore, the application of modern technology in medicine largely depends on this research.