The paper discusses optimization issues of training Artificial Neural Networks (ANNs) using a nonlinear trigonometric polynomial function. The proposed method presents the mathematical model of an ANN as an information transmission system where effective techniques to restore signals are widely used. To optimize ANN training, we use energy characteristics assuming ANNs as data transmission systems. We propose a nonlinear layer in the form of a trigonometric polynomial that approximates the “syncular” function based on the generalized approximation theorem and the wave model. To confirm the theoretical results, the efficiency of the proposed approach is compared with standard ANN implementations with sigmoid and Rectified Linear Unit (ReLU) activation functions. The experimental evaluation shows the same accuracy of standard ANNs with a time reduction of the training phase of supervised learning for the proposed model.