DESIGN OF FIRST ORDER DIFFERENTIATOR WITH PARALLEL ALL-PASS STRUCTURE

Goran Stančić, Ivan Krstić, Saša S. Nikolić, Ivana Kostić

DOI Number
https://doi.org/10.22190/FUACR230324004S
First page
039
Last page
055

Abstract


In this paper a new method for design of the first order differentiator is presented. The proposed differentiator consists of two parallel branches, i.e. direct path and IIR all-pass filter. The described design method allows one to obtain solution with minimum mean relative error at the desired region by controlling the ratio of phase response extremes. A small relative magnitude error, as well as a low phase error, at low frequencies is condition for good time domain behaviour. The obtained differentiator can be realized by means of only two multipliers, hence being a good choice for real time applications. The proposed solution provides a lower magnitude error than several known differentiators with similar phase error.

Keywords

Recursive differentiator, all-pass filters, approximately linear phase, parallel structure, minimum multiplications

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References


R. C. Nongpiur, D. J. Shpak, and A. Antoniou, “Design of IIR digital differentiators using constrained optimization”, IEEE Transactions on Signal Processing, vol. 62, no. 7, pp. 1729-1739, 2014. doi: 10.1109/TSP.2014.2302733

O. P. Goswami, T. K. Rawat, and D. K. Upadhyay, “A novel approach for the design of optimum IIR differentiators using fractional interpolation”, Circuits, Systems, and Signal Processing, vol. 39, pp. 1688-1698, 2020. doi: 10.1007/s00034-019-01211-0

M. A Al-Alaoui, “Novel approach to designing digital differentiators”, Electronics Letters, vol. 28, no. 15, pp. 1376-1378, 1992. doi: 10.1049/el:19920875

M. A Al-Alaoui, “Novel digital integrator and differentiator”, Electronics Letters, vol. 29, no. 4, pp. 376-378, 1993. doi: 10.1049/el:19930253

S.-C. Pei and H. Hsu, “Fractional bilinear transform for analog-to-digital conversion”, IEEE Transaction on Signal Processing, vol. 56, no. 5, pp. 2122-2127, 2008. doi: 10.1109/TSP.2007.912250

L.-C. Tsai and K.-C. Chu, “Design of first-order differentiator and integrator using bilinear transformations”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E92-A, no. 3, pp. 928-931, 2009. doi: 10.1587/transfun.E92.A.928

L. D. Milić, M. D. Lutovac, and J. D. Ćertić, “Design of first-order differentiator utilising FIR and IIR sub-filters”, International Journal of Reasoning-based Intelligent Systems vol. 5, no. .1, pp. 3-11, 2013. doi: 10.1504/IJRIS.2013.055122

R. Barsainya and T. K. Rawat, “Novel design of recursive differentiator based on lattice wave digital filter”, Radioengineering, vol. 26, no. 1, pp. 387-395, 2017. doi: 10.13164/re.2017.0387

D. K. Upadhyay, “Class of recursive wideband digital differentiators and integrators”, Radioengineering, vol. 21, no. 3, pp. 904-910, 2012.

D. K. Upadhyay, “Recursive wideband digital differentiators”, Electronics Letters, vol. 46, no. 25, pp. 1-2, 2010.

N. Q. Ngo, “A new approach for the design of wideband digital integrator and differentiator”, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 9, pp. 936-940, 2006. doi: 10.1109/TCSII.2006.881806

G. Stančić, I. Krstić, and S. Cvetković, “All-pass-based design of nearly-linear phase IIR low-pass differentiators”, International Journal of Electronics, vol. 107, no. 9, pp. 1451-1470, 2020. doi: 10.1080/00207217.2020.1726498

G. Stančić, I. Krstić, and M. Živković, “Design of IIR fullband differentiators using parallel all-pass structure”, Digital Signal Processing, vol. 87, pp. 132-144, 2019. doi: 10.1016/j.dsp.2019.01.026

G. Stančić, M. Đurić, B. Jovanović, and S. Cvetković, “A complexity analysis of IIR filters with an approximately linear phase”, Radioengineering, vol. 28, no. 2, pp. 430-438, 2019. doi: 10.13164/re.2019.0430

S. R. Sankranti, T.K. Battula, and M.R. Veera, “Design and implementation of first order digital differentiators at microwave frequencies”, American Journal of Signal Processing, vol. 5, no.3, pp. 56-58, 2015. doi: 10.5923/j.ajsp.20150503.02

S. Nikolić, G. Stančić, and S. Cvetković, “Realization of digital filters with complex coefficients”, FACTA UNIVERSITATIS: Series Automatic Control and Robotics, vol. 17, no. 1, pp. 25-38, 2018. doi: 10.22190/FUACR1801025N

M. Đurić, G. Stančić, and M. Živković, “A new method for design of selective digital IIR filters with arbitrary phase”, FACTA UNIVERSITATIS: Series Automatic Control and Robotics, vol. 17, no. 3, pp. 191-204, 2018. doi: 10.22190/FUACR1803191D

S. R. Sankranti, T. K. Battula, and M. R. Veera, “Design and implementation of first order digital differentiators at microwave frequencies”, American Journal of Signal Processing, vol. 5, no. 3, pp. 56-58, 2015. doi: 10.5923/j.ajsp.20150503.02

B. T. Krisha and S. S. Rao, “On design and applications of digital differentiators”, Proceedings of the On design and applications of digital differentiators, Anna University, Chennai, India, December 13.-15., 2012, pp. 1-7. doi: 10.1109/ICoAC.2012.6416802




DOI: https://doi.org/10.22190/FUACR230324004S

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