New Savitzky-Golay Digital Differentiator of Fractional Order

This brief proposes a design method aims for a new Savitzky-Golay digital differentiator of fractional order (SGDFO), which generalizes the Savitzky-Golay filter from the integer order to the fractional order for estimating the fractional order derivative of the contaminated signal. The proposed method calculates the moving window’s weights using the polynomial least-squares method and the Riemann- Liouville fractional order derivative definition. and then computes the fractional order derivative of the given signal using the convolution between the weights and the signal, instead of the complex mathematical deduction. Hence, the computation time is greatly improved. Frequency-domain analysis reveals that the proposed differentiator is essentially a fractional order low-pass filter. Results out of the experiments demonstrate that the proposed SGDFO can accurately estimate the fractional order derivatives of both noise-free signal and contaminated signal.