Signal Reconstruction Using New Biorthogonal Frequency-Modified Kravchenko Wavelets When Representing the Measurement Process as a Convolution Model
Viktor F. Kravchenko, В. И. Пустовойт, A. V. Yurin · Journal of Communications Technology and Electronics · 2020
Abstract—A new biorthogonal system of wavelet bases has been constructed, which is oriented toward reconstructing the useful signal of a measuring system if the measurement process is represented as a convolution model. New biorthogonal wavelet bases are obtained by using a instrumental function to modify a Kravchenko orthogonal wavelet system with a finite spectrum. The properties of new biorthogonal frequency-modified wavelets are studied, and digital filters that realize fast computational algorithms are constructed. Schemes for multiresolution analysis are proposed, which, during discrete wavelet transform, immediately solve the problem of reconstructing the useful signal, as well as effective noise suppression, which can significantly speed up computations.