Abstract
The effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous wavelet analysis compared to a pure signal. Therefore, the identification of a real signal by using a continuous color wavelet spectrogram is difficult. To solve this problem, for the first time, a comparative analysis of spectrograms of signals and correlation matrices is carried out. The spectrograms of signals are obtained based on continuous wavelet transformation in the form of images with areas of different colors of variable intensity. Correlation matrices are computed by using mathematical functions of the coefficients of discrete wavelet spectra.
Similar content being viewed by others
References
Y. N. Klikushin, V. Y. Kobenko, "Fundamentals of identification measurements," Radio Electron. J., n.5 (2006). URI: http://jre.cplire.ru/iso/nov06/index.html.
A. K. Lagirvandze, A. N. Kalinichenko, T. V. Morgunova, "ECG cycles forms analysis based on machine learning techniques," Model. Syst. Networks Econ. Technol. Nature, Soc., n.4, p.75 (2019). URI: https://cyberleninka.ru/article/n/algoritm-analiza-form-kardiotsiklov-ekg-s-ispolzovaniem-tehnologiy-mashinnogo-obucheniya/viewer.
D. A. Kuzin, L. G. Statsenko, P. N. Anisimov, M. M. Smirnova, "Applying machine learning methods to acoustic signal classification using spectrum characteristics," Izv. SPBGETU “LETI,” n.3, p.48 (2021).
M. S. Salman, A. Eleyan, B. Al-Sheikh, "Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix," TELKOMNIKA (Telecommunication Comput. Electron. Control., v.18, n.6, p.3073 (2020). DOI: https://doi.org/10.12928/telkomnika.v18i6.16191.
T. Hu, J. Zhao, S. Yan, W. Zhang, "Performance analysis of a wavelet packet transform applied to concrete ultrasonic detection signals," J. Phys. Conf. Ser., v.1894, n.1, p.012062 (2021). DOI: https://doi.org/10.1088/1742-6596/1894/1/012062.
V. O. Braun, V. P. Dolgushin, V. N. Loza, I. V. Pampukha, "Investigation of possibilities and characteristics of methods for reducing noise level in signal processing based on use of wavelet technology," Radio Electron. J., n.7 (2014). URI: http://jre.cplire.ru/jre/jul14/6/text.html.
Y. K. Taranenko, V. V. Lopatin, O. Y. Oliynyk, "Wavelet filtering by using nonthreshold method and example of model Doppler function," Radioelectron. Commun. Syst., v.64, n.7, p.380 (2021). DOI: https://doi.org/10.3103/S0735272721070049.
G. Galati, G. Pavan, F. De Palo, "Chirp signals and noisy waveforms for solid-state surveillance radars," Aerospace, v.4, n.1, p.15 (2017). DOI: https://doi.org/10.3390/aerospace4010015.
D. O. Hogenboom, C. A. DiMarzio, "Quadrature detection of a Doppler signal," Appl. Opt., v.37, n.13, p.2569 (1998). DOI: https://doi.org/10.1364/AO.37.002569.
L. Debnath, "The Gabor Transform and Time-Frequency Signal Analysis," in Wavelet Transforms and Their Applications (Birkhäuser Boston, Boston, MA, 2002). DOI: https://doi.org/10.1007/978-1-4612-0097-0_4.
M. Kovačević, "Signaling to relativistic observers: an Einstein–Shannon–Riemann encounter," Probl. Inf. Transm., v.56, n.4, p.303 (2020). DOI: https://doi.org/10.1134/S0032946020040018.
P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, Y. Vázquez-Baeza, et al., "SciPy 1.0: fundamental algorithms for scientific computing in Python," Nat. Methods, v.17, n.3, p.261 (2020). DOI: https://doi.org/10.1038/s41592-019-0686-2.
S. K. Goh, H. A. Abbass, K. C. Tan, A. Al-Mamun, C. Wang, C. Guan, "Automatic EEG artifact removal techniques by detecting influential independent components," IEEE Trans. Emerg. Top. Comput. Intell., v.1, n.4, p.270 (2017). DOI: https://doi.org/10.1109/TETCI.2017.2690913.
B. Belkacemi, S. Saad, Z. Ghemari, F. Zaamouche, A. Khazzane, "Detection of induction motor improper bearing lubrication by discrete wavelet transforms (DWT) decomposition," Instrum. Mes. Métrologie, v.19, n.5, p.347 (2020). DOI: https://doi.org/10.18280/i2m.190504.
Y. K. Taranenko, "Methods of discrete wavelet filtering of measuring signals: an algorithm for choosing a method," Izmer. Tekhnika, n.10, p.14 (2021). DOI: https://doi.org/10.32446/0368-1025it.2021-10-14-20.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
ADDITIONAL INFORMATION
Y. Taranenko, N. Rizun
The authors declare that they have no conflicts of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
The initial version of this paper in Russian is published in the journal “Izvestiya Vysshikh Uchebnykh Zavedenii. Radioelektronika,” ISSN 2307-6011 (Online), ISSN 0021-3470 (Print) on the link http://radio.kpi.ua/article/view/S0021347022020042 with DOI: https://doi.org/10.20535/S0021347022020042
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Radioelektronika, No. 2, pp. 110-125, February, 2022 https://doi.org/10.20535/S0021347022020042 .
About this article
Cite this article
Taranenko, Y., Rizun, N. Wavelet Filtering of Signals without Using Model Functions. Radioelectron.Commun.Syst. 65, 96–109 (2022). https://doi.org/10.3103/S0735272722020042
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0735272722020042