**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.

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**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)