Method of localized signal reconstruction in dynamic environments based on modified Volterra series

Abstract

The paper presents a comprehensive study and development of an adaptive method for signal reconstruction in dynamic environments. The proposed method is based on the use of modified Volterra series with temporal constraints, where the contribution of kernels is limited by local time windows defined using a smoothing Gaussian function. This approach overcomes the limitations of traditional spectral methods, which, due to the smoothing effect, are unable to accurately reproduce transient or impulsive features of the signal. To detect critical areas of the signal, an instability indicator is introduced, enabling selective activation of the time-limited model only in unstable zones. In stable regions of the signal, reconstruction is carried out using a frequency model, ensuring efficient use of computational resources. Experimental results show an increase in the local coherence coefficient (ALC) in the range of 10–14%, depending on the spatial localization of critical points and the intensity of temporal signal changes, as well as a decrease in the mean squared error (MSE) by 12–18% compared to traditional frequency-based reconstruction methods. The obtained results confirm the effectiveness of the proposed method for signal processing in cognitive telecommunications systems under complex noise conditions