"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki)  ISSN 1684-1719, N 2, 2017 contents             full text:  pdf

Numerical differentiation of biomedical signals based on wavelet transform

B. Z. Garmaev, V .V. Boronoev

Institute of Physical Material Science of the Siberian branch of RAS, Sakhyanovoy 6 str., Ulan-Ude 670047, Russia

The paper is received on February 7, 2017

Abstract. The paper shows the method of numerical differentiation of noisy biomedical signals based on wavelet transform with Haar wavelet. The main feature of this method is that for differentiation it is not necessary to calculate an inverse wavelet transform. It significantly reduces the computational cost. It allows using this method for the analysis of long-term signals and real-time analysis. For differentiation we use the wavelet coefficients at certain scales, multiplied by the factor and divided by the sampling rate. The factor is calculated for each scale separately for the least value of the difference between wavelet coefficients and the true derivative. Next, we search scale with the smallest difference between the calculated and the true derivative. The selection of these parameters is the regularization of wavelet differentiation. For biomedical signals, which are taken from one place with the use of one instrument, it is necessary to search these parameters only once, and further, it is possible to recover the derivative using the found factor and scale. The simplicity of the method and the regularization allows to implement the algorithm in hardware of medical devices. The accuracy of this method was compared with accuracy of known methods for two characteristic signals. The accuracy of this method is comparable to the accuracy of standard wavelet differentiation. Standard wavelet differentiation requires about three times more computing, because it requires calculation of inverse wavelet transform. Thus, this simplification of the algorithm of wavelet differentiation did not decrease the accuracy of the derivative reconstruction.

Key words: numerical differentiation, wavelet transform, regularization, Haar wavelet.

References

1.       Boronoev, V.V, Shabanova, E.V. Numerical differentiation of the radical artery sphygmogram by tikhonov regularization. Measurement Techniques. 1994, Vol. 37, No. 11, pp. 1307-1312.

2.       Patrickeyev, I.A., Stepanov, R.A., Frick, P.G. Wavelet differentiation of noisy signals. Vychislitel'nye metody i programmirovanie - Numerical Methods and Programming. 2005, Vol. 6, pp. 35-42. (In Russian)

3.       Boronoyev, V.V., Rinchinov, O.S. Methods of Spline Approximation in the Problem of Amplitude-Time Analysis of a Pulse Wave. Radiophysics and Quantum Electronics. 1998, Vol. 41, No. 8, pp. 706-715.

4.       Boronoyev, V.V., Garmaev, B.Z., Lebedintseva, I.V. The features of continuous wavelet transform for physiological pressure signals. Optika Atmosfery i Okeana - Optics of atmosphere and ocean. 2007, Vol. 20, No. 12, pp. 1142-1146. (In Russian)

5.       Boronoyev, V.V., Garmaev, B.Z., Lebedintseva, I.V. The features of continuous wavelet transform for physiological pressure signal. Proc. SPIE. 2008, Vol. 6936, No. 693611.

6.       Boronoyev, V.V., Garmaev, B.Z. Wavelet-Based Method of Pressure Signal Components Detection. Biomedicinskiya radioehlektronika - Biomedical Radioelectronics. 2009, No. 3, pp. 44-49. (In Russian)

7.       Boronoev, V.V., Garmaev, B.Z. Wavelet-based Detection Method for Physiological Pressure Signal Components. Proceedings of 2014 International Conference on Computer Technologies in Physical and Engineering Applications (ICCTPEA). pp. 23-24.

8.       Paul Horowitz, Winfield Hill The art of electronics. Cambridge University Press, 1980.

9.       Pereberin, A.V. Systematization of wavelet transforms. Vychislitel'nye metody i programmirovanie - Numerical Methods and Programming. 2001, Vol. 2, pp. 15-40. (In Russian)

10.  Stankovic, R.S., Falkowski, B.J. The Haar wavelet transform: its status and achievements. Computers and Electrical Engineering. 2003, Vol. 29, pp. 25-44.

For citation:

B.Z.Garmaev, V.V.Boronoev. Numerical differentiation of biomedical signals based on wavelet transform. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 2. Available at http://jre.cplire.ru/jre/feb17/9/text.pdf. (In Russian)