RegLS-Separation Filter

Design of a digital filter for separating a signal into its periodic and aperiodic signal components

"RegLS - Separation Filter" demonstrates the design of a digital filter suitable for separating a signal into its periodic and aperiodic portions. The filter design/tuning is based on a Regularized Least Squares (RegLS) approach.

Two distinctive features of this approach are its ability to separate signals into periodic and aperiodic components while removing measurement noise, and its capability to compute confidence measures for the extracted components.

The filter design and application is demonstrated on a synthetic dataset.

The toolbox contains the following support functions:

• harmonicBasis.m: creates a matrix with harmonic basis functions.

This code can also be considered as supplemental Material to the Paper:

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

by: Johannes Handler, Matthew Harker and Dimitar Ninevski

October 2024

Abstract:

This paper introduces a novel 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 with 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 provided, and the method is validated using both real-world measurement data from an industrial process and synthetic datasets.

@unpublished{Handler2024,

author = {Johannes Handler, Matthew Harker and Dimitar Ninevski},

title = {A Regularized Least-Squares Approach to Digital Filter Design for Periodic and Aperiodic Signal Separation},

year = {2025},

booktitle={2025 European Control Conference (ECC)},

doi={submitted}}

Related work,

@inproceedings{Handler2023,

author={Handler, Johannes and Ninevski, Dimitar and O'Leary, Paul},

title={Modelling Periodic Measurement Data Having a Piecewise Polynomial Trend Using the Method of Variable Projection},

booktitle={IECON 2023- 49th Annual Conference of the IEEE Industrial Electronics Society},

year={2023},

pages={1-8},

doi={10.1109/IECON51785.2023.10312537}}

@inproceedings{Handler2021,

author={Handler, Johannes and Ninevski, Dimitar and O'Leary, Paul},

title={Decomposition of a Periodic Perturbed Signal with Unknown Perturbation Frequency by the Method of Variable Projection},

booktitle={2021 7th International Conference on Mechanical Engineering and Automation Science (ICMEAS)},

year={2021},

pages={44-49},

doi={10.1109/ICMEAS54189.2021.00019}}