Regeneration of discrete signals missing samples in the internet of things applications at digital information transmitting via infocommunication channels

Abstract

The paper discusses a method for recovering missing samples of an analog signal during transmission over communication channels in applications of the Internet of Things. The aim of the work is to obtain a mathematical description of the procedure for restoring the values of the signal samples from the output of the analog sensor on the receiving side, which were not transmitted in order to reduce the load on data transmission channels. The procedure is based on the well-known principles of adaptive signal processing, based on the dynamic determination of the parameters of digital filters based on the assessment of the least-mean-square (LMS) deviation of the signal passing through the filter from a reference signal obtained in one way or another. A feature of the proposed method is the solution of the inverse problem of restoring the samples of the original signal with the known parameters of the filter and the reference signal. In this work, the problem of skipping and restoring samples of a discrete signal is formulated, an expression is obtained for the objective function of the method for restoring missing discrete samples, as well as an expression for iterative restoration by Newton's method of the values of the samples of the original analog signal on the receiving side, which were not transmitted via the data transmission channel. The conditions for the applicability of the method are established, which consist in the a priori known parameters of the reference signal and the digital filter, which are determined in advance from the known characteristics of the original signal. Filtration and transmission of electrocardiogram signals through communication channels, for which an electrocardiogram can be obtained as a reference form, as the norm for healthy patients, is considered as a problem for the solution of which the proposed method is applicable. The practical significance of the proposed method lies in the organization of distributed computing for IoT systems, for which it is critically important to ensure energy savings of an autonomous power source for sensors and reduce the load on data transmission channels.