Fractal Signal Processing

doi:10.1007/s00034-025-03338-9

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Fractal Signal Processing

2025-09-01

PRE

Alireza Khalili Golmankhaneh *

Diana T. Pham

Rawid Banchuin

Hamdullah Şevli̇

DOI：10.1007/s00034-025-03338-9

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Abstract

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This paper presents a novel low-pass filtering framework based on Fractal First \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order and Second \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order designs, formulated within the framework of fractal calculus. By incorporating the structure of fractal time, the proposed filters can effectively process signals with intricate, non-differentiable characteristics. The fractal second \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order low-pass filter is applied to a simulated noisy ECG signal, demonstrating significant noise suppression while preserving the essential morphological features of the waveform. A comparative study with the classical Bessel low-pass filter further illustrates the advantages of the fractal approach in capturing scale-invariant and self-similar properties of biomedical signals. These results highlight the potential of fractal-order filters for advanced biomedical signal processing.

Keywords:

Low-pass filter

Fractal filter

ECG signal processing

Fractal alpha-order filter