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Design of Low-Pass Digital Differentiators Based on B-splines
Zijun He, Yining Sun
Pages - 30 - 42     |    Revised - 01-06-2014     |    Published - 01-07-2014
Volume - 8   Issue - 3    |    Publication Date - July 2014  Table of Contents
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KEYWORDS
Low-pass Differentiator, B-spline, Finite-impulse Response (FIR), Digital Filters.
ABSTRACT
This paper describes a new method for designing low-pass differentiators that could be widely suitable for low-frequency signals with different sampling rates. The method is based on the differential property of convolution and the derivatives of B-spline bias functions. The first order differentiator is just constructed by the first derivative of the B-spline of degree 5 or 4. A high (>2) order low-pass differentiator is constructed by cascading two low order differentiators, of which the coefficients are obtained from the nth derivative of a B-spline 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 anti-noise capability of the proposed differentiators. These properties analysis and simulations indicate that the proposed differentiator can be applied to a wide range of low-frequency signals, and the trade-off between noise- reduction and signal preservation can be made by selecting the maximum allowable value of a.
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Dr. Zijun He
Department of Automation, University of Science and Technology of China - China
hezijun@mail.ustc.edu.cn
Dr. Yining Sun
Institute of Intelligent and Machines - China