A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si29.svg"> <mml:mrow> <mml:mi>℘</mml:mi> </mml:mrow> </mml:math> -order R-L high-pass filter modeled by local fractional derivative
Kang‐Jia Wang, Cuiling Li
Abstract
As an important electronic device, filter is applied to all kinds of electronic products. In this paper, a new ℘-order R-L High-pass filter (HPF) modeled by the local fractional derivative (LFD) is proposed for the first time. With the help of the local fractional Laplace transform (LFLT), we obtain the non-differentiable(ND) transfer function, and present the expressions of ND amplitude-frequency characteristic (AFC) and ND phase-frequency characteristics (PFC). The corresponding parameters and properties of the ℘-order R-L HPF are also studied. What’s interesting is that the ℘-order R-L HPF becomesthe ordinary one in the exceptional case at ℘ = 1. The obtained results in this paper reveal the sufficiency of the local fractional derivative for analyzing the circuit systems in fractal space.