On The Theory And Applications Of Hilbert-Huang Transform

The theory of Hilbert-Huang Transform is brought forward by Norden E Huang as a new method of time-frequency analysis in 1998. In the theory, any siginal can be decomposed through the method of Empirical Mode Decompsition, and written in the form of sum of several Intrinsic Mode Functions and a residual function. Then the time-frequency analysis about these IMFs is carried on through the method of Hilbert-Transform, and instantaneous frequencies can be derived. Hilbert-Huang Transform shows its efficiency and auto-adaptability in many occasions especially in the analysis and processing of non-linear or non-stationary signals. It has become an excellent signal analytical tool of many advantages and great potential.On the basis of a great deal of researches in the past about the theory and applications of Hilbert-Huang Transform, effors are made trying to improve and develop its theory. Starting from the concept of instantaneous frequency and the model of signals, the notion of local narrowband signal is proposed in this letter, and explained as the essence of IMF, with the Process of EMD also described as one of time-varient narrow-band filtering.Furthermore, more detailed and more deeply arguments are presented towards the relevant problems which have been discussed before, or which exist now still. Special attentions and researches are paid on the problems about the endpoint extension, orthogonality and minimal signal period. These problems are described, explained and solved from a new and different perspective. Therefore, the theoretical system of the scientific Hilbert-Huang Transform is consolidated and developed.Besides, as the 2-Dimensional extension of Hilbert-Huang Transform, the main methods of 2-Dimensional Empirical Mode Decomposition (BEMD and 2D-EMD) are summarized. Concrete modified algorithms practical into use are presented in this letter, and the theory and research relevant to analytical analysis for 2-Dimensional signals are also introduced briefly.Finally in the last chapter, the methods of 2-Dimensional Empirical Mode Decomposition are put into practical use to solve the problems about the processing of 2-D digital images including the details Extraction, the Edge Detection and the DCT Compression of the images. The experimental results of these applications have validated (shown) its efficiency and excellent performance. Consequently, the applications of Hilbert-Huang transform in the field of 2-Dimensional signals are expanded into a more popular situation.