Fractional Order Numerical Differentiation with B-Spline Functions

Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the Tikhonov regularization problem. Then, we propose a fractional order differentiator by calculating the fractional derivative of the obtained smoothing spline. Numerical results are given to show the efficiency of the proposed method in comparison with some existing methods.

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