This textbook presents the basics of the Fourier, the Gabor and the continuous wavelet analysis with the Morlet wavelet. The course started from the theoretical derivation based on the averaging approach, which is close connected with corresponding methods in the theory of dynamical systems. Thus, the introductory Chapter 1 is supplied with the examples illustrating analogies between the considered signal processing and the analytical approximations for ODE solutions. Chapter 2 explores the representation of the continuous wavelet transform with the Morlet wavelet as a solution of partial differential equations. Chapter 3 contains the practical recipes for MATLAB’s code realizing the described algorithms and the examples of their implementations.
Учебное пособие представляет основы преобразований Фурье, Габора и непрерывного вейвлет-преобразования с вейвлетом Морле. Курс начинается с теоретического вывода, основанного на подходе усреднения, который тесно связан с соответствующими методами в теории динамических систем. Таким образом, вводная Глава 1 сопровождается примерами, иллюстрирующими аналогии обработки сигналов и аналитических аппроксимаций для решений ОДУ. Глава 2 исследует представление непрерывного вейвлет-преобразования с вейвлетом Морле как решения дифференциальных уравнений в частных производных. Глава 3 содержит практические рецепты программного кода для MATLAB, реализующего описанные алгоритмы, и примеры их применения.
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