Regularized Fractional Order Integration and Differentiation Via Discrete Orthogonal Polynomials

Abstract

In this paper, we present a new approach for the regularized fractional order integration and differentiation of signals containing noise. The method combines the highly efficient and accurate piecewise (local) approximation of a signal using discrete orthogonal polynomials, and their fractional order integrals. The method provides a vast improvement in accuracy over the traditional method of using non-regularized formulae, or using global polynomial approximation. The method is demonstrated on a periodic signal over several periods with a high level of synthetic noise.