This paper presents a novel low-pass filtering framework based on Fractal First \(\alpha\) -order and Second \(\alpha\) -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 \(\alpha\) -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.
