The fractal active low-pass filter within the local fractional derivative on the Cantor set
ISSN: 0332-1649
Article publication date: 8 February 2023
Issue publication date: 23 November 2023
Abstract
Purpose
The purpose of this paper is to derive a new fractal active low-pass filter (LPF) within the local fractional derivative (LFD) calculus on the Cantor set (CS).
Design/methodology/approach
To the best of the author’s knowledge, a new fractal active LPF within the LFD on the CS is proposed for the first time in this work. By defining the nondifferentiable (ND) lumped elements on the fractal set, the author successfully extracted its ND transfer function by applying the local fractional Laplace transform. The properties of the ND transfer function on the CS are elaborated in detail.
Findings
The comparative results between the fractal active LPF (for γ = ln2/ln3) and the classic one (for γ = 1) on the amplitude–frequency and phase–frequency characteristics show that the proposed method is correct and effective, and is expected to shed light on the theory study of the fractal electrical systems.
Originality/value
To the best of the author’s knowledge, the fractal active LPF within the LFD calculus on the CS is proposed for the first time in this study. The proposed method can be used to study the other problems in the fractal electrical systems, and is expected to shed a light on the theory study of the fractal electrical systems.
Keywords
Acknowledgements
This work is supported by the Key Programs of Universities in Henan Province of China (22A140006), the Fundamental Research Funds for the Universities of Henan Province (NSFRF210324), Program of Henan Polytechnic University (B2018-40), the Innovative Scientists and Technicians Team of Henan Provincial High Education (21IRTSTHN016).
Declaration of interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.
Citation
Wang, K.-J. (2023), "The fractal active low-pass filter within the local fractional derivative on the Cantor set", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 6, pp. 1396-1407. https://doi.org/10.1108/COMPEL-09-2022-0326
Publisher
:Emerald Publishing Limited
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