UDC 53.088.3+53.088.7
FILTERING AND COMPRESSION OF SIGNALS BY THE METHOD OF DISCRETE WAVELET
TRANSFORMATION INTO ONE-DIMENSIONAL SERIES
Abstract. Solving the problem of identifying special signals under a priori uncertainty of their sources is extremely important, for example, when detecting locators working on moving objects. The method is used for filtering signals from powerful noises (up to 12dB) and determining the shape of the signal. The identification, filtering, and compression of signals based on the comparison of the proximity of one-dimensional series of wavelet coefficients are considered. The article proposes a direct transformation of nested arrays of the approximation and detail coefficients into a one-dimensional series with a preliminary determination of the structure of the nested arrays for further reconstruction of the one-dimensional series into an identifiable measurement signal. The robustness of the proposed algorithm to local changes in the shape of the test signal in accordance with the identification requirements is verified.
Keywords: identification measurements, row proximity measures, one-dimensional series, discrete wavelet analysis, linear and non-linear modulation, database.
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REFERENCES
- Lagirvandze A.K., Kalinichenko A.N., Morgunova T.V. Algorithm for analyzing forms of ECG cardiocycles using machine learning technologies. Models, systems, networks in economics, technology, nature, and society. 2019. N 4 (32). P. 75–84.
- Kuzin D.A., Statsenko L.G., Anisimov P.N., Smirnova M.M. Application of machine learning methods for the classification of acoustic signals by spectral characteristics. Informatics, computer technology, and management. Izvestiya SPbGETU "LETI". 2021. N 3. P. 48–53.
- Salman M.S., Eleyan A., Al-Sheikh B. Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix. TELKOMNIKA. 2020. Vol. 18, N 6. P. 3073–3079. https//doi.org/10.12928/telkomnika.v18i6.16191.
- Galati G., Pavan G., De Palo F. Chirp signals and noisy waveforms for solid-state surveillance radars. Aerospace. 2017. Vol. 4, N 1. P. 15. https://doi.org/10.3390/aerospace4010015.
- Hogenboom D.O., DiMarzio C.A. Quadrature detection of a Doppler signal. Applied Optics. 1998. Vol. 37, Iss. 13. P. 2569–2572. URL: https://www.osapublishing.org/ao/abstract.cfm?URI=ao-37-13-2569 .
- Debnath L. The Gabor transform and time-frequency signal analysis. In: Wavelet Transforms and Their Applications. Boston, MA: Birkhuser, 2015. P. 257–306. https://doi.org/10.1007/ 978-1-4612-0097-0_4.
- M. Signaling to relativistic observers: an Einstein–Shannon–Riemann encounter. Problems of Information Transmission. 2020. Vol. 56, N 4. P. 303–308.
- Voskoboynikov Yu.E., Gochakov A.V., Kolker A.B. Filtering signals and images: Fourier and wavelet algorithms (with examples in Mathcad) [in Russian]. Novosibirsk: NGASU (Sibstrin), 2010. 188 p.
- Mallat S.G. Multiresolution approximations and wavelet orthonormal bases of L? (R). Transactions of the American Mathematical Society. 1989. Vol. 315, N 1. P. 69–87.
- Mallat S. A theory of multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 1989. Vol. 11, N 7. P. 674–693.
- NumPy Array manipulation: ndarray.flatten() function. URL: https://www.w3resource.com/numpy .
- Taranenko Yu.K. Methods of discrete wavelet filtering of measuring signals: an algorithm for choosing a method. Izmeritel'naya tekhnika. 2021. N 10. P. 14–20. https://doi.org/10.32446/0368-1025it.2021-10-14-20.
- Burnaev E.V., Olenev N.N. Proximity measure for time series based on wavelet coefficients. Proc. XLVIII scientific. conf. MIPT. Dolgoprudny: FUPM, 2005. P. 108–110.
- Taranenko Y.K., Lopatin V.V., Oliynyk O.Y. Wavelet filtering by using nonthreshold method and example of model Doppler function. Radioelectronics and Communications Systems. 2021. Vol. 64, N 7. P. 380–389.
- Klikushin Yu.N., Kobenko V.Yu. Fundamentals of identification measurements. Journal of Radio Electronics. 2006. N. 5. P. 6. URL: http://jre.cplire.ru/iso/nov06/index.html .
- Taranenko, Y., Rizun, N. Wavelet filtering of signals without using model functions. Radioelectronics and Communications Systems. 2022. Vol. 65, N 2. P. 96–109.
- Burnaev E.V. Application of wavelet transform for the analysis of economic time series. Mathematical modeling of developing economic systems. Proc. Summer School on Economic and Mathematical Modeling ECOMOD. 2006. Vol. 2006. P. 95.
