Fractional-Order FIR Differentiators with Optimum Noise Attenuation

Design and implementation of a class of fractional-order digital FIR differentiators is described. The design approach is based on optimizing the white noise attenuation of the differentiator while assuming a polynomial signal model of a limited order. The approach avoids the noise amplification problem of many other approximations by limiting the differentiation bandwidth. A computationally efficient recursive structure makes it possible to implement the FIR differentiator with very few multipliers regardless of the length of the impulse response.