The paper deals with theory questions, as well as examples of calculations based on modern basis functions with compact carriers for solving problems of forming discrete samples of continuous signals with finite energy. The method is based on the law of asymptotic attenuation of the values of the wavelet coefficient moduli to zero as n → ∞, and the speed of their motion to zero depends on the choice of the wavelet. This method can be defined as the summation of the octave energy components of the coefficients of fast wavelet transformations with the binary law of decreasing sampling steps.
1. K.Blatter, “Wavelet analysis. Fundamentals of the theory”, Moscow: The technosphere, 2006. 272 p.
2. N, Ahmed, K.Rao, “Orthogonal transformations in the processing of digital signals”, Trans. with English. M.: Communication. 1980, 248 p.
3. I.M.Dremin, O.V.Ivanov, V.A.Nechitailo, “Wavelets and their use”, Uspekhi Fizicheskikh Nauk, vol. 171, no. 5, pp. 465-501, 2001.
4. A.K.Novikov, “Polyspectral analysis”, Sank Peterburg.: Central Research Institute of Krylov, 2000, 162 p.
5. S.F.Svinyin, “Theory and methods of forming samples of signals with infinite spectra”, Sank Peterburg: Nauka, 2016, 71 p.
6. Hakimjon Zayniddinov, Madhusudan Singh, Dhananjay Singh, “Polynomial Splines for Digital” Signal and Systems (Monograph in English), LAMBERT Academic publishing, Germany, 2016 year, 208 p.
7. H.N.Zainidinov, “Methods and means of signal processing in piecewise polynomial bases”, Monograph, Tashkent "Fan technology" 2014, 190 p.
8. H.N.Zaynidinov, Dannanjay Singh, Hoon Jae Lee, “Piecewise quadratic Harmut basis function and their applications to problems in digital signal processing”, International Journal of Communication Systems, John Wiley & Sons, Ltd., DOI: 10,1002 dac.1093, Jan. 2010, London, SCIE. www.interscience.wiley.com
9. S. Malla, "Wavelets in signal processing", Moscow, "Peace", 2005
Zaynidinov, H.N; Zaynutdinova, M.B; and Yusupov, I.
"Application of wavelets for forming discrete selections of continuous signals.,"
Chemical Technology, Control and Management: Vol. 2018
, Article 42.
Available at: https://uzjournals.edu.uz/ijctcm/vol2018/iss3/42