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Highly noisy signal waveform restoration based on integro-differential transform and integral curve approximation

In the field of digital signal processing, restoring their shape at a high level of noise component is one of the main problems. Its relevance is due to the widespread use of digital technologies and it becomes particularly acute in those areas where interference inevitably affects the registration quality, recognition, and signals interpretation. A common type of naturally occurring interference is thermal noise, which is directly related to the measuring operation and recording equipment. It is impossible to completely eliminate this noise kind, but modern digital processing methods are capable of significantly reducing its negative impact. Currently, researchers’ attention is increasingly focused on developing heuristic algorithms that represent alternative ways of suppressing the noisy component while preserving the useful signal’s form. These algorithms are characterized by their ability to find approximate solutions where traditional analytical and technical methods lose their effectiveness. They are aimed at adapting to the stochastic nature of thermal noise and offer a reasonable compromise between labor intensity and the useful signal reproduction accuracy. This article continues previous published research into the heuristic algorithms development for recovering the shape of heavily distorted discrete signals. The goal is to propose an alternative approach to solving this problem based on the sequential application idea of numerical integration and differentiation operations combined with integral curve approximation procedure. As a result, the noise component influence is eliminated, and the restored signal retains information components of the useful signal. The proposed algorithm efficiency was determined using a test signal superimposed with artificial noise simulated via computer simulation of a pseudo-random number generator. The results were compared with two previously developed heuristic algorithms: one based on piecewise linear approximation by least squares method and another based on averaging instantaneous values of the signal over partition intervals. Analysis demonstrated that the developed algorithm compares favorably in terms of accuracy with these algorithms, but differs in greater efficiency when processing discrete nonperiodic signals with natural noise contamination. Read more...