Computing Semilinear Sparse Models for Approximately Eventually Periodic Signals

TL;DR

This paper introduces a method for modeling approximately eventually periodic signals using a combination of sparse representations, linear autoregressive models, and neural networks, enabling effective signal approximation after initial aperiodic behavior.

Contribution

It presents a novel approach that combines sparse, linear, and neural network models to effectively approximate signals with initial aperiodic phases followed by periodic behavior.

Findings

Successful modeling of approximately eventually periodic signals.

Effective sparse representation of model parameters.

Prototypical implementations demonstrate practical viability.

Abstract

Some elements of the theory and algorithmics corresponding to the computation of semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic discrete-time signals, that is, signals that can exhibit an aperiodic behavior for an initial amount of time, and then become approximately periodic afterwards. The semilinear models considered in this study are obtained by combining sparse representation methods, linear autoregressive models and GRU neural network models, initially fitting each block model independently using some reference data corresponding to some signal under consideration, and then fitting some mixing parameters that are used to obtain a signal model consisting of a linear combination of the previously fitted blocks using the aforementioned reference data, computing sparse representations of some of the matrix parameters of the resulting model along the process. Some prototypical computational implementations are presented as well.