Orthogonality Of The Hht Emd Method

Hilbert-Huang Transform is a new signal processing method, proposed by Norden E Huang and others in 1998, and has been widely used in engineering. In this theory, firstly decomposing the signal into a series of intrinsic mode function (IMF) by the empirical mode decomposition (EMD) method, secondly analysising the intrinsic mode function (IMF) by Hilbert spectral analysis, and then getting the final result, Hilbert spectrum. Hilbert-Huang transform has good adaptability, and can well process nonlinear and nonstationary signals, so it is excellent and potential for signal processing.However, because this is a new method, the mathematical theory has not been completed for the Hilbert-Huang Transform, so there are many problems in the method. For example, the mode mixing problem occured after the EMD decomposition is one of them. And whether the EMD decomposition method has the orthogonality, the question has not been solved in theory.This thesis describes the theoretical basis of Hilbert-Huang Transform, and investigates the mode mixing problem. As the actual signal usually contain noise, so there will be the phenomena of mode mixing among IMF components after the EMD decomposition. Essentially each component in the IMF should only contain a characteristic scale of the signal component, but the mode mixing occures, so there will be a phenomenon, that a component in the IMF contains signal components of other IMF components, and this shall be the mode mixing. The mode mixing will result the physical meaning of the IMF components is unclear, and affects the next analysis. This thesis attempts to use KL transform to remove the mode mixing, and verifies the validity of the method by examples.Finally, on the basis of KL transform removes the mode mixing, verifying whether all modes are orthogonal before mixing and after mixing. Based on the verifying, proving that EMD method is orthogonal.