Standard and singular wavelet analysis
https://doi.org/10.21122/2309-4923-2020-4-39-44
Abstract
The paper suggests that the use of classical wavelets may be auxiliary in the analysis of a periodic signal. This is because the intuitive interpretation of the wavelet transform is not obvious. It is proposed to consider the Fourier transform as the main tool in applied research of periodic signals. An example is provided to support this point of view. To isolate the periodic component of the signal, along with wavelet analysis, it is proposed to perform spectral analysis. To do this, pre-filtering is performed using singular wavelets. This approach can significantly complement classical wavelet analysis.
About the Authors
V. M. Romanchak
Belarusian National Technical University
Belarus
Belarus
Associate Professor, PhD in Physics and Mathematics, Engineering Mathematics department
Minsk
M. A. Hundzina
Belarusian National Technical University
Belarus
Belarus
Associate Professor, PhD in Physics and Mathematics, Engineering Mathematics department
Minsk
References
1. Marple, S. L. Digital spectral analysis and its applications / S. L. Marple. – М.: Mir, 1990. –584 p.
2. Chewy, K. Introduction to wavelets / K. Chewy. – М.: Mir, 2001. – 412 p.
3. Dobeshi, I. Ten lectures on wavelets. / I. Dobeshi. Izhevsk: SRC “RCD”, 2001. – 464 p.
4. Dyakonov, V. P. Wavelets. From theory to practice / V. P. Deacons. – M .: SOLONPress, 2004. – 400 с.
5. Romanchak, V. M. Approximation by singular wavelets / V. M. Romanchak // System analysis and applied informatics, 2018. – No. 2. – P. 23–28.
6. Romanchak V. M. Local transformations with a singular wavelet / V. M. Romanchak // Computer Science, 2020. – V. 17. – No.1. – P. 39–46.
7. Romanchak V. M. Singular wavelets on a finite interval / V. M. Romanchak // Informatika, 2018. – T. 15. – No. 4. – P. 39–49.
8. Kulachev, A. P. Critique of the wavelet analysis of the EEG / A. P. Kulachev // Actual problems of the humanities and natural sciences, 2016. – V. 1. – No. 12. – P. 47–57.
9. Kulachev, A. P. Computer electrophysiology and functional diagnostics / A. P. Kulaichev. – M.: FORUM–INFRA-M, 2016. – 640 p.
10. Komorowski, D. The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings / D. Komorowski, S. Pietraszek // J. Med. Syst. – V. 40. – No. 10. – 2016. doi: 10.1007/s10916–015–0358–4.
Review
For citations:
Romanchak V.M., Hundzina M.A. Standard and singular wavelet analysis. «System analysis and applied information science». 2020;(4):39-44. (In Russ.) https://doi.org/10.21122/2309-4923-2020-4-39-44
Views:
503
Email this article 