Down-sampling Theory Of Non-linear Adaptive Signal Based On Empirical Mode Decomposition

In the era when most data are non-stationary and non-linear,fast and efficient processing of non-stationary non-linear signals plays an important role in the academic research and industrial applications of signal processing.In 1998,Huang N E proposed the Hilbert-Huang Transform,and the empirical mode decomposition(Empirical Mode Decomposition,EMD),one of the core parts of the Hilbert-Huang Transform,gradually became an important tool in the field of non-stationary nonlinear signal processing and analysis.Different from the traditional time-frequency analysis methods that use harmonic components to approximate signals,the Empirical Mode decomposition does not need to preset the basis function in advance.It can decompose the signal into multiple IMFs adaptively according to its own time characteristics.In other words,EMD can be applied to different signals,and therefore is widely used in many different fields.But empirical decomposition also raises a related issue: oversampling.For discrete time signals,the length of the Intrinsic Mode Functions is equal to the length of the input signal.The signal is decomposed into multiple Intrinsic Mode Functions,so the total number of discrete points of all Intrinsic Mode Functions is usually greater than the length of the input signal.To solve the over-sampling problem,we carried out the following work:(1)This paper innovatively proposed an optimal adaptive non-uniform filter bank design method for extracting the Intrinsic Mode Functions.Firstly,the adaptive gradient is used to learn each Intrinsic Mode Functions,and the corresponding passband and inhibitory band of each Intrinsic Mode Functions in the frequency domain are obtained.The original signal is reconstructed by the optimal adaptive non-uniform filter Banks.Finally,we transform the filter bank design problem into a semi-infinite programming problem and solve it.The advantages of the proposed method are as follows: first,the method is based on the adaptive gradient to obtain the sampling value and the passband range,which can make full use of the advantages of EMD in processing nonlinear and non-stationary signals.Second,this method can ensure that the reconstructed signal and the original signal can obtain a lower sampling rate within the allowable error and reduce the oversampling problem.(2)This method can realize very small reconstruction error under very small oversampling rate.In addition,in order to prove that the proposed filter bank design can fully experience the non-linearity and non-stationarity of empirical mode decomposition,two mixed sinusoidal signals with large difference in frequency of gaussian noise were used for experimental comparison.Although the frequency of the signal component changes greatly and the sampling integer and filter need to be redesigned,the total number of the inherent modal functions remains unchanged and the over-sampling rate is approximately the same,which indicates the robustness of the proposed method.