Application of neural networks to reconstruct a continuous representation of a signal from discrete samples taken at random moments in time

Digital signal processing in cyber-physical technological systems is based on algorithms that operate with information presented in a discretized form both by level and by time. In the latter case, the constancy of the time quantization interval is assumed as one of the postulated conditions for the application of algorithms. At the same time, in practice, such constancy is not always ensured, which leads to the omission of individual samples or even to a random nature of the discretization. Therefore, an urgent research task is to develop methods and algorithms for signal processing under conditions of random discretization, in particular, for the restoration of continuous signals from their discrete samples taken with violation of the requirements of the Kotelnikov – Shannon theorem. If the discretization interval of a continuous signal is calculated taking into account its requirements (i. e. discretization is carried out with a frequency not lower than the Nyquist frequency), then its exact restoration from discrete samples is allowed, otherwise it is impossible. However, even for this situation, there are approaches to the restoration of continuous signals that take into account additional a priori information about the nature of the signal. Some of these approaches are based on complex mathematical apparatus, which makes them difficult to apply and not universal, while others use deep machine learning models that are expensive in terms of computational resources and demanding in terms of training data volumes. Under these conditions, a method is proposed for restoring a signal with a limited spectrum from discrete samples, the time interval between which is random, and its mathematical expectation is greater than the value determined by the Kotelnikov – Shannon theorem for regular discretization. The novelty of the research results lies in the proposed method and algorithm for restoring a continuous signal, as well as in the results of the analysis of a numerical experiment conducted with a software model executed in the MatLab environment and implementing the developed algorithm.