Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
Volume 58, Issue 11, Pages 758-762Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSII.2011.2168022
Keywords
Digital differentiator; fractional order derivative; least-squares method; Savitzky-Golay filter
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Funding
- National Natural Science Foundation of China [61174145]
- China Scholarship Council
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This brief proposes a design method for a digital fractional order Savitzky-Golay differentiator (DFOSGD), 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. Experiments demonstrate that the proposed DFOSGD can accurately estimate the fractional order derivatives of both noise-free signal and contaminated signal.
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