Influence of Wilbraham-Gibbs Phenomenon on Digital Stochastic Measurement of EEG Signal Over an Interval

Open access

Abstract

Measurement methods, based on the approach named Digital Stochastic Measurement, have been introduced, and several prototype and small-series commercial instruments have been developed based on these methods. These methods have been mostly investigated for various types of stationary signals, but also for non-stationary signals. This paper presents, analyzes and discusses digital stochastic measurement of electroencephalography (EEG) signal in the time domain, emphasizing the problem of influence of the Wilbraham-Gibbs phenomenon. The increase of measurement error, related to the Wilbraham-Gibbs phenomenon, is found. If the EEG signal is measured and measurement interval is 20 ms wide, the average maximal error relative to the range of input signal is 16.84 %. If the measurement interval is extended to 2s, the average maximal error relative to the range of input signal is significantly lowered - down to 1.37 %. Absolute errors are compared with the error limit recommended by Organisation Internationale de Métrologie Légale (OIML) and with the quantization steps of the advanced EEG instruments with 24-bit A/D conversion

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Teplan M. (2002). Fundamentals of EEG measurement. Measurement Science Review 2 (2) 1-11.

  • [2] Bronzino J.D. (2000). Principles of electroencephalography. In Bronzino J.D. (ed.) Biomedical Engineering Handbook (2nd ed.). CRC Press 1-13.

  • [3] Webster J.G. (1998). Medical Instrumentation Application and Design (11th ed.). Wiley.

  • [4] Abeles M. Goldstein M. (1977). Multispike train analysis. Proceedings of the IEEE 65 (5) 762-773.

  • [5] Winter B.B. Webster J.G. (1983). Driven-right-leg circuit design. IEEE Transactions on Biomedical Engineering 30 (1) 62-66.

  • [6] Kutz M. (2003). Standard Handbook of Biomedical Engineering and Design. McGraw-Hill.

  • [7] Schnitz B.A. Stewart J.A. Allen R.V. Fadem K.C. (2004). Improving signal quality and test reliability in EEG measurements using integrated high-density surface-mount electronics. http://ebook.lib.sjtu.edu.cn/smat/Files/S2-3.pdf.

  • [8] Teplan M. Krakovska A. Štolc S. (2003). EEG in the context of audiovisual stimulation. Measurement Science Review 3 (2) 17-20.

  • [9] Teplan M. Krakovska A. Štolc S. (2006). Shortterm effects of audio-visual stimulation on EEG. Measurement Science Review 6 (4) 67-70.

  • [10] Krakovska A. Štolc S. (2006). Fractal complexity of EEG signal. Measurement Science Review 6 (4) 63-66.

  • [11] Šušmakova K. Krakovska A. (2007). Classification of waking sleep onset and deep sleep by single measures. Measurement Science Review 7 (4) 34-38.

  • [12] Šušmakova K. (2006). Correlation dimension versus fractal exponent during sleep onset. Measurement Science Review 6 (4) 58-62.

  • [13] von Neumann J. (1956). Probabilistic logic and the synthesis of reliable organisms from unreliable components. In Shannon C. McCarthy J. (eds.) Automata Studies. Princeton University Press 43-98.

  • [14] Wagdy M.F. Ng W. (1989). Validity of uniform quantization error model for sinusoidal signals without and with dither. IEEE Transactions on Instrumentation and Measurement 38 (3) 718-722.

  • [15] Kamensky M. Kovač K. (2011). Correction of ADC errors by additive iterative method with dithering. Measurement Science Review 11 (1) 15-18.

  • [16] Vujičić V. Milovančev S. Pešaljević M. Pejić D. Župunski I. (1999). Low frequency stochastic true RMS instrument. IEEE Transactions on Instrumentation and Measurement 48 (2) 467-470.

  • [17] Pejic D. Vujicic V. (2000). Accuracy limit of highprecision stochastic Watt-hour meter. IEEE Transactions on Instrumentation and Measurement 49 (3) 617-620.

  • [18] Santrač B. Sokola M.A. Mitrović Z. Župunski I. Vujičić V. (2009). A novel method for stochastic measurement of harmonics at low signal-to-noise ratio. IEEE Transactions on Instrumentation and Measurement 58 (10) 3434-3441.

  • [19] Pjevalica V. Vujičić V. (2010). Further generalization of the low-frequency true-RMS instrument. IEEE Transactions on Instrumentation and Measurement 59 (3) 736-744.

  • [20] Antić B.M Mitrović Z.L Vujičić V.V. (2012). A method for harmonic measurement of real power grid signals with frequency drift using instruments with internally generated reference frequency. Measurement Science Review 12 (6) 277-285.

  • [21] Angeloneb L.M. Purdona P.L. Ahveninena J. Belliveaua J.W. Bonmassara G. (2006). EEG/(f)MRI measurements at 7 Tesla using a new EEG cap (“InkCap”). NeuroImage 33 (4) 1082-1092.

  • [22] Negishi M. Pinus B.I. Pinus A.B. Constable R.T. (2007). Origin of the radio frequency pulse artifact in simultaneous EEG-fMRI recording: Rectification at the carbon-metal interface. IEEE Transactions on Biomedical Engineering 54 (9) 1725-1727.

  • [23] Mirsattari S.M. Ives J.R. Leung S. Menon R.S. (2007). EEG monitoring during functional MRI in animal models. Epilepsia 48 (4) 37-46.

  • [24] Allen P.J. Josephs O. Turner R. (2000). A method for removing imaging artifact from continuous EEG recorded during functional MRI. NeuroImage 12 (2) 230-239.

  • [25] Sovilj P.M. Milovančev S.S. Vujičić V. (2011). Digital stochastic measurement of a nonstationary signal with an example of EEG signal measurement. IEEE Transactions on Instrumentation and Measurement 60 (9) 3230-3232.

  • [26] Sovilj P. Vujičić V. Pjevalica N. Pejić D. Urekar M. Župunski I. (2013). Influence of signal stationarity on digital stochastic measurement implementation. Electronics 17 (1) 45-53.

  • [27] Wilbraham H. (1848). On a certain periodic function. The Cambridge and Dublin Mathematical Journal 3 198-201.

  • [28] Gibbs J.W. (1899). Fourier's series. Nature 59 (1539) 606.

  • [29] Hazewinkel M. (2001). Gibbs phenomenon. In Encyclopedia of Mathematics. Springer.

  • [30] Smith S.W. (1999). The Scientist and Engineer's Guide to Digital Signal Processing (2nd ed.). California Technical Publishing 141-168.

  • [31] International Organization of Legal Metrology. (1990). Electroencephalographs - Metrological characteristics - Methods and equipment for verification. OIML R 89 Edition 1990 (E).

  • [32] g.tec - Guger Technologies http://www.gtec.at.

  • [33] Compumedics Neuroscan http://compumedicsneuroscan.com/products-overview/.

Search
Journal information
Impact Factor

IMPACT FACTOR 2018: 1.122
5-year IMPACT FACTOR: 1.157

CiteScore 2018: 1.39

SCImago Journal Rank (SJR) 2018: 0.325
Source Normalized Impact per Paper (SNIP) 2018: 0.881

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 108 50 2
PDF Downloads 53 33 0