The research is devoted to the use of artificial neural networks (ANN) for signal processing. The features of the simplest feed forward neural networks (multilayer perceptrons, MLP) application are analyzed. When using MLP in a sliding time window, it allows to solve problems of signal approximation with high accuracy and to determine their parameters when analyzing dynamic processes. If the signal can be set by analytical formulas with random parameters on separate time intervals, then after training, MLP can be implemented in microprocessor equipment for real-time signal processing. The ANN training algorithms and the errors of the proposed signal processing method are discussed. The approach does not require "deep learning" and a complex ANN structure, it allows one to control the accuracy of algorithms at intermediate stages of calculations. The results are of interest for electrical engineering and smart energy systems.