A Regularized Least-Squares Approach to Digital Filter Design for Periodic and Aperiodic Signal Separation

This paper introduces a new digital filter design approach for separating signal mixtures into periodic and aperiodic components using a regularized least-squares framework. The framework models the aperiodic component using a geometric polynomial, while the periodic component is represented through trigonometric functions. By incorporating a regularization term within the least-squares formulation, the method effectively preserves signal fidelity and prevents overfitting. The digital filter coefficients are obtained by solving the regularized least-squares problem. Additionally, this approach allows for the calculation of confidence intervals for the extracted signal components, providing a measure for the reliability of the results.A comprehensive analysis of the model parameters is carried out, and the method is validated using both real-world measurement data from an industrial process and synthetic datasets.