Estimation of the error of a homomorphic filter for multiplicatively interacting signals and sampling windows during periodic estimation.

The article is a further development of the authors' research in the field of information transmission systems, specifically the method of concentrating integral transformations. The object of study is one of the dominant factors leading to the limitation of information transmission speed over communication channels. This is intersymbol distortion or intersymbol interference. Previously, to reduce intersymbol distortions, the authors proposed a homomorphic filter. Its application allows the multiplicatively interacting information signal and the sampling window to be represented additively, as well as to isolate the error caused by the intersymbol interference itself. This error is the key factor that necessitates the reduction of information transmission speed. In the present article, an analysis of the described homomorphic filter is conducted, and an assessment of the error of the homomorphic filter for multiplicatively interacting signals and sampling windows under periodic evaluation is performed. The task of finding an estimate of the effectiveness of the formed homomorphic filter is solved by a method based on the use of an asymptotic approach. The main result presented in this work is an analytical estimate of the level of intersymbol interference of an asymptotic type for the adopted research model. The novelty lies in the obtained asymptotic estimate of the level of intersymbol distortions, which are the main factor limiting the speed of information transmission. It should also be noted that intersymbol interference is not only a problem for communication channels of classical data transmission systems but also a rapidly developing issue in the currently emerging G5 cellular networks. The article provides a generalized estimate of the level of intersymbol distortions for the model of a communication channel in the form of an ideal low-pass filter and rectangular data windows. Based on a simplified model of the behavior of this type of error, a partial estimate of the level of intersymbol interference of an asymptotic type is obtained.