On the method of approximation and quantization of information transmission through communication channels

Abstract

This article discusses the issues of information transmission over communication channels based on an adjacent algorithm for signal approximation and sampling. The nature of the communication channel is described, which is a set of technical means for transmitting messages from one point in space to another. It is proved that the transmission is most often carried out in conditions of unavoidable interference. From this point of view, to eliminate gaps, an approximation method is used for a continuous message converted into an electrical form of the primary x(t), which can be converted into a discrete form (sequence of numbers) using the process of taking samples at certain intervals. It is proved that from a practical point of view, the intervals are taken to be the same and equal to a certain value. The mathematical expectation of quantization noise is used to determine interference and signal quality. Legendre's interpolation polynomial is used to reconstruct the signals. The computational procedure for adaptive sampling can be implemented in hardware. The introduction substantiates the relevance of the publication of this scientific article based on the analysis of the available scientific results of scientific research in the field of signal processing and transmission by quantization and approximation. The summary lists the results obtained in the framework of scientific research and discusses their theoretical and practical significance.