Application of Discrete Wavelet Transform and Convolution to Find the Values of Locally Approximated Splines

Yu.I. Bityukov, doctor of technical sciences, professor of the Moscow Aviation Institute (National Research University), Moscow
Yu. I. Deniskin, doctor of technical sciences, professor of the Moscow Aviation Institute (National Research University), Moscow
G.Yu. Deniskina, graduate student of the Moscow Aviation Institute (National Research University), Moscow
e-mail: dega17@yandex.ru
 
Algorithms for finding the values of locally approximating n-variable splines and their partial derivatives using a discrete wavelet transform and a convolution operation are considered. The results are applied to the estimation of the values of the partial derivatives of the functions specified at the grid nodes and to the problem of local modification of the surface of an aircraft engine fan blade made of composite materials using the automated calculation method.
Keywords: Splines, wavelet transform, local surface modification, automated layout, composite materials.
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DOI: 10.34214/2312-5209-2020-27-3-39-45