Operators to calculate the derivative of digital signals

• 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
• Download:

  IMEKO-TC4-2013-076.pdf
• DOI:

  _unreg_tc4-2013.076

Event details:

• IMEKO TC:

  TC4
• Event name:

  TC4 Symposium 2013
• Title:

  19th IMEKO TC4 Symposium Measurements of Electrical Quantities (together with 17th TC4 IWADC Workshop on ADC and DAC Modelling and Testing)
• Place:

  Barcelona, SPAIN
• Time:

  18 July 2013 - 19 July 2013