Design and application of variable fractional order differentiator

Abstract

In this paper, the design problem and application of the variable fractional order differentiator (VFOD) are investigated. First, the Cauchy integral formula is generalized to define the fractional derivative of function. Then, the weighted least squares method is presented to design FIR variable fractional order differentiator. Finally, VFOD is applied to synthesize and analyze 1/f noise process. Simulation results demonstrate that the proposed method can generate more accurate 1/f noise than the conventional fractional differencing method