Research On The Local-instantaneous Signal Analysis Theory Of The Hilbert-Huang Transform

The Hilbert-Huang transform (HHT) is a new theory, which is first developed by Huang et al at the end of last century, for the signal analysis. The main innovations embodied in this method are the present of the concept of the intrinsic mode (IMF) and introduction of the method of empirical sifting method (EMD). A signal is first decomposed into often finite IMFs by the EMD, and then, with the Hilbert transform, the meaning instantaneous frequencies of every IMF is obtained which give precise description of the varying frequency. The final presentation of the result is an energy-frequency-time distribution, designated as the Hilbert spectrum. We can also further get marginal spectrum of the signal. The HHT is highly efficient since it is based on the local characteristic of a signal and adaptive. It is very applicable to analyze nonlinear and non-stationary signal which frequency is variable with time. The varying frequency is a natural phenomenon in the actual life that is often felt by people. The essential aim of the HHT is to describe this phenomenon and uncover its law, that is, to look for the instantaneous frequency of a signal. However, the HHT adaptively takes advantage of the local information of a signal at a certain time to obtain the instantaneous frequency of the signal at that time. The amount, which appears an instantaneous value but in fact has adaptive local information of a signal, is called Local-instantaneous amount in this paper, and the signal analysis theory by which some Local-instantaneous amounts is obtained is called Local-instantaneous signal analysis. For showing this characteristic, this paper further calls the HHT as the Hilbert-Huang transform Local-instantaneous signal analysis (HHT-LISA).The HHT-LISA has important theoretical value and widely applying perspective. It has effectively been applied in some actual engineering problems. However, this theory appears very late since its first public literature wasn't published until 1998. Many works need to be done to perfect and improve it. Based on the former works done by Huang et al, using the study method of jointing physical meaning, theoretical induction and program validation, this paper relatively deeply and thorough studied the HHT-LISA. Some achievements are achieved and the HHT-LISA was further perfected. The HHT-LISA is a new problem in all at present moment. Although the studies on the varying frequency were begun very early, most of these subsequent works are translated to indirectly uncover this phenomenon by time-frequency joint analysis andadopt integral method to analyze it. These works are all based on the Fourier analysis theory. The Fourier theory is earliest and most perfect one for signal analysis, and it also first adopted frequency spectrum analysis method. However, the frequency of the Fourier analysis is independent of time since it is defined by a whole sine signal. Fourier analysis will suffer the shortcomings such as dummy signal and dummy frequency. Certainly, the time-frequency joint analysis of a signal based on the Fourier analysis theory will also suffer the same shortcomings. They can't also arrive at the aim to precisely describe the law of varying frequency with time because of the Heisenberg indefinite principle. The HHT-LISA directly studies instantaneous frequency and precisely describes its law. Furthermore, it adopts differential method to analyze it, so its applied value is largely increased. Of course the difficult degree is also largely increased. In order to deeply and detailedly study this all-new problem, this paper first gives a introduction to the historical perspective of signal analysis, Fourier analysis and time-frequency analysis before direct introduction and study on the HHT-LISA. The difference between people's straight feel and the result of Fourier analysis and time-frequency analysis and its reason are deeply analyzed in this paper. These works shows people's thirst for the instantaneous frequency analysis theory and the difficulty to obtain it.Subsequent...