The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations



непрерывные вейвлет-преобразования, вейвлет Морле, гауссовы вейвлеты, уравнение диффузии, уравнения в частных производных


The usage of partial differential equations for the evaluation of a wavelet transform with real and complex wavelets and with vanishing higher moments is considered. Contrary to the case of the transform with the standard Morlet wavelet, the sought-for transform can be found as a superposition of solutions to several Cauchy problems with various initial values. These initial values are the products of a transformed function with some power functions whose exponents vary from zero to the maximal number of a vanishing moment.

Author Biography

E.B. Postnikov

Kursk State University,
Faculty of Physics and Mathematics


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How to Cite

Постников Е.Б. The Representation of a Wavelet Transform of the Gaussian Family by a Superposition of Solutions to Partial Differential Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2008. 9. 84-89



Section 1. Numerical methods and applications