Исследование изменений энтропии и энергии на этапах декомпозиции сигнала

Abstract

RU: Проведено исследование поведения энтропии и энергии сигнала на этапах его декомпозиции. Предложен метод разделения исходного сигнала сложной формы на независимые составляющие с помощью математического аппарата вейвлет-преобразования и теории информации. UK: Проведено дослідження виявлення змін ентропії та енергії сигналу на етапах його декомпозиції. Запропоновано метод ділення сигналу складної форми на незалежні складові за допомогою математичного апарату вейвлет-перетворення та теорії інформації. EN: Research of changes of entropy and energy on signal decomposition is presented. Coifman’s method for the purpose for signal delineation was modified. The method of complex signal delineation based on wavelet transformation and information theory is proposed. The algorithm for the signal components separation is developed. The proposed method based on research of total entropy of both signal formed components. The first component is the reconstructed source signal after wavelet transformation on the current decomposition level in which the approximation coefficients must be equals to zero. The second component is the residue from the deduction of the source signal and the second component on the current decomposition level. The turning point of the total entropy curve denotes the most unstable system state in which the components can be identified. The most unstable system state is system state having zero increment of information. Entropy increments until the turning point and it decrease after. The sum of the sinusoids was used as test signal. The results of the method have high accuracy.