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This paper describes a new method for designing lowpass differentiators that could be widely suitable for lowfrequency signals with different sampling rates. The method is based on the differential property of convolution and the derivatives of Bspline bias functions. The first order differentiator is just constructed by the first derivative of the Bspline of degree 5 or 4. A high (>2) order lowpass differentiator is constructed by cascading two low order differentiators, of which the coefficients are obtained from the nth derivative of a Bspline of degree n+2 expanded by factor a. In this paper, the properties of the proposed differentiators were presented. In addition, we gave the examples of designing the first to sixth order differentiators, and several simulations, including the effects of the factor a on the results and the antinoise capability of the proposed differentiators. These properties analysis and simulations indicate that the proposed differentiator can be applied to a wide range of lowfrequency signals, and the tradeoff between noise reduction and signal preservation can be made by selecting the maximum allowable value of a.
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