Firstly the one-dimension digital fractional order Savitzky-Golay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure robust and accuracy. Experiments demonstrate that 1-D DFOSGD can estimate the fractional order derivatives of both ideal signal and noisy signal accurately. Secondly, the two-dimension DFOSGD is obtained from 1-D DFOSGD by defining a group of direction operators, and a new image enhancing method based on 2-D DFOSGD is presented. Experiments demonstrate that 2-D DFOSGD has very good performance on image enhancement.

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