Fractional order differentiator using legendre polynomials

In this paper, a discrete time fractional order differentiator has been modeled for estimating the fractional order derivatives of contaminated signal based on Legendre's polynomials. The given signal is approximated with Legendre polynomials of different degrees. The Riemann-Liouville (R-L) fractional order derivative definition is used. For finding the fractional order derivatives of signal, first of all, window weight corresponding to required fractional order is calculated. In second step, calculated window weight is convolved with the signal. Several test signals are considered for validation of the proposed method. The proposed method performs better for noisy data also.