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Fractional Band-Pass Filters: Design, Implementation and Application to EEG Signal Processing

AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

E-mail Address: jb@agh.edu.pl

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Paweł Piątek

AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

E-mail Address: ppi@agh.edu.p

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https://doi.org/10.1142/S0218126617501705Cited by:34 (Source: Crossref)

Abstract

Fractional band-pass filters are a promising area in the signal processing. They are especially attractive as a method for processing of biomedical signals, such as EEG, where large signal distortion is undesired. We present two structures of fractional band-pass filters: one as an analog of classical second-order filter, and one arising from parallel connection of two fractional low-pass filters. We discuss a method for filter implementation — Laguerre Impulse Response Approximation (LIRA) — along with sufficient conditions for when the filter can be realized with it. We then discuss methods of filter tuning, in particular we present some analytical results along with optimization algorithm for numerical tuning. Filters are implemented and tested with EEG signals. We discuss the results highlighting the possible limitations and potential for development.

This paper was recommended by Regional Editor Piero Malcovati.

Keywords:

References

1. A. G. Radwan, A. S. Elwakil and A. M. Soliman, On the generalization of second-order filters to the fractional-order domain, J. Circuits Syst. Comput. 18 (2009) 361–386. Link, Web of Science, Google Scholar
2. R. Stanisławski, K. J. Latawiec, M. Gałek and M. Łukaniszyn, Modeling and identification of fractional-order discrete-time laguerre-based feedback-nonlinear systems, Advances in Modelling and Control of Non-integer-Order Systems, eds. K. J. Latawiec, M. Łukaniszyn and R. Stanisławski, Lecture Notes in Electrical Engineering 320 (Springer International Publishing, 2015), pp. 101–112. Google Scholar
3. R. Stanisławski, K. Latawiec, M. Galek and M. Łukaniszyn, Modeling and identification of a fractional-order discrete-time siso laguerre-wiener system, in 19th Int. Conf. Methods and Models in Automation and Robotics (MMAR), 2014, September 2014, pp. 165–168. Google Scholar
4. T.-B. Deng, Discretization-free design of variable fractional-delay fir digital filters, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 48 (2001) 637–644. Web of Science, Google Scholar
5. D. Sierociuk and A. Dzielinski, New method of fractional order integrator analog modeling for orders 0.5 and 0.25, in 16th Int. Conf. Methods and Models in Automation and Robotics (MMAR), 2011, August 2011, pp. 137–141. Google Scholar
6. G. Tsirimokou, C. Laoudias and C. Psychalinos, 0.5-v fractional-order companding filters, Int. J. Circuit Theory Appl. (2014) n/a–n/a. Web of Science, Google Scholar
7. G. Tsirimokou, C. Psychalinos and A. S. Elwakil, Emulation of a constant phase element using operational transconductance amplifiers, Analog Integr. Circuits Signal Process. 85 (3) (2015) 413–423. Web of Science, Google Scholar
8. G. Maione, Laguerre approximation of fractional systems, Electron. Lett. 38 (2002) 1234–1236. Web of Science, Google Scholar
9. M. Aoun, R. Malti, F. Levron and A. Oustaloup, Synthesis of fractional laguerre basis for system approximation, Automatica 43 (9) (2007) 1640–1648. Web of Science, Google Scholar
10. P. Bania, J. Baranowski and M. Zagórowska, Convergence of Laguerre impulse response approximation for non-integer order systems, Math. Probl. Eng. 2016 (Article ID 9258437) (2016) p. 13. Web of Science, Google Scholar
11. J. Baranowski, W. Bauer, M. Zagórowska and P. Piątek, On digital realizations of non-integer order filters, Circuits Syst Signal Process 35 (6) (2016) 2083–2107. Web of Science, Google Scholar
12. W. Bauer and A. Kawala-Janik, Implementation of bi-fractional filtering on the arduino uno hardware platform, Lect. Notes Electr. Eng. 407 (2017) 419–428. Google Scholar
13. G. Ferri, V. Stornelli and A. Di Simone, A CCII-based high impedance input stage for biomedical applications, J. Circuits Syst. Comput. 20 (08) (2011) 1441–1447. Link, Web of Science, Google Scholar
14. R. VanRullen, Four common conceptual fallacies in mapping the time course of recognition, Front Psychol. 2 (2011) 365. Web of Science, Google Scholar
15. D. J. Acunzo, G. MacKenzie and M. C. van Rossum, Systematic biases in early ERP and ERF components as a result of high-pass filtering, J. Neurosci. Methods 209 (1) (2012) 212–218. Web of Science, Google Scholar
16. A. Widmanna, E. Schrögera and B. Maessb, Digital filter design for electrophysiological data — a practical approach, J. Neurosci. Methods 250 (2015) 34–36. Web of Science, Google Scholar
17. A. Broniec, Analysis of eeg signal by flicker-noise spectroscopy: Identification of right-/left-hand movement imagination, Med. Biol. Eng. Comput. 54 (12) (2016) 1935–1947. Web of Science, Google Scholar
18. P. Piątek, J. Baranowski, M. Zagórowska, W. Bauer and T. Dziwiński, Bi-fractional filters, part 1: Left half-plane case, in Advances in Modelling and Control of Noninteger-order Systems - 6th Conference on Non-Integer Orfer Caculus and its Applications, eds. K. J. Latawiec, M. Łukaniszyn and R. Stanisławski (Springer, 2014). Google Scholar
19. A. Ali, A. Radwan and A. Soliman, Fractional order butterworth filter: Active and passive realizations, IEEE J. Emerg. Sel. Top. Circuits Syst. 3 (2013) 346–354. Web of Science, Google Scholar
20. D. Matignon, Stability properties for generalized fractional differential systems, ESAIM Proc. 5 (1998) 145–158. Google Scholar
21. D. Matignon, Stability results for fractional differential equations with applications to control processing, Comput. Eng. Syst. Applic. (1996). Google Scholar
22. Chebfun — numerical computing with functions http://www.chebfun.org. Google Scholar