Design of variable and adaptive fractional order FIR differentiators

In this paper, the design problems of variable and adaptive fractional order finite impulse response (FIR) differentiators are investigated. First, the fractional differencing method and weighted least squares (WLS) approach are presented to design variable fractional order differentiators which can be implemented by the efficient Farrow structure. Next, an adaptive fractional order differentiator is developed and applied to estimate the parameters of 1/f noise from the finite observation data set. The parameters are updated by using least mean squares (LMS) adaptive algorithm. Finally, the variable fractional order differentiator is used to reduce the error rate of handwritten signature verification system.