Algorithm for calculating the wavelet-transform of the signals using the chebyshev-hermit functions
The paper deals with the development of basis for computation wavelet-transform from the coefficients given by decomposition original signal with Chebyshev-Hermite functions. Decomposition with Chebyshev-Hermite functions allow to transform original signal into coefficients, that can be used for reconstructing different transforms of original signal like Fourier transform, derivatives of different orders, wavelet transform and others. These transforms can be obtained by using corresponding bases that need to be created. In this paper considered basis for wavelet-transform with derivative of arbitrary order of the Gauss functions as analyzing wavelet. This basis is computed by applying continuous wavelet transform with derivative of Gauss functions as analyzing wavelet into the Chebyshev-Hermite functions. Arrays of the wavelet coefficients are presented as 3D plots. The Mathematica 11.3 computer algebra system was used to calculations and graph the results.