Operators to calculate the derivative of digital signals

Lluis Ferrer-Arnau, Juan Mon Gonzalez, Vicenç Parisi-Baradad

Abstract

This paper presents an FIR operator with a very low computational cost for calculating the first derivative of discrete band-limited signals. The basic idea is to use cubic spline polynomials for interpolating among the samples and estimate the derivative of the discrete signal as a derivative of the polynomial. This method also allows estimating the derivative at the points between samples. The main contribution of this work is to develop a highly efficient FIR operator with only 9 coefficients for implementing the derivative operator algorithm. The resulting filter can be easily implemented in a microcontroller or an FPGA since only 5 additions and 3 fixed-point multiplications are necessary. If the frequency range of the input signal is between 0 and 0.2 times the sampling frequency (taking 5 samples per cycle), the maximum error in calculating the derivative does not exceed 1.03 %.

Keywords

first derivative operator, cubic B-splines, FIR filters, low computational cost, detecting singular points of a discrete signal, DA conversion

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DOI

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IMEKO TC

TC4 - Measurement of Electrical Quantities

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