Application of homomorphic filtering for multiplicatively interacting signals and data sampling windows during periodic evaluation

Abstract

The object of the study is information transmission systems. Improving the quality of information on the receiving side is considered as the subject of the study. The authors consider in detail such aspects of the topic as the formation of a procedure that significantly reduces the influence of intersymbol interference caused by the interaction of the signal itself and the sampling window. This source of errors, as a rule, is dominant at information transfer rates close to the bandwidth of the communication channel. Studies on reducing the influence of intersymbol distortions are important and relevant, and in recent years a significant number of works have been devoted to them. A signal model simulating the transmission of a sequence of non-modulated pulses of the meander type was considered. It was assumed that the processing of the incoming pulse stream is carried out in real time based on the procedures of periodic evaluation of each element. The methodological basis of the research was the methods of mathematical modeling of information transmission systems and linearization methods using the generalized superposition principle. The main result of the conducted research is the proposed method of forming a homomorphic filter for processing the incoming pulse stream in real time based on the procedures of periodic evaluation of each element. The algorithm of its functioning ensures the transformation of the multiplicative interaction of the signal and the sampling windows into an additive one and ensures the separation of the multiplicatively interacting transmitted information signal and the sampling window in the communication channel. The resulting procedure, which reduces the effect of intersymbol interference on the receiving side, is an implementation of an optimal filter based on a homomorphic transformation. An estimate of the magnitude of intersymbol interference is obtained when using the proposed processing method. The effectiveness of the method in signal streaming processing is demonstrated. The expressions are obtained in the most general form and can be detailed within the framework of the described information transfer model, which is the subject of further research.