Study On Time-Frequency Analysis Method Based On Empirical Mode Decomposition

Now, time-frequency analysis is one of the top interests in Signal Processing,and more and more research has been put on this topic. And time-frequencyanalysis based on Empirical Mode Decomposition (EMD) is a new two-steptime-frequency analytic method to process nonlinear and non-stationary signal.The key step of this method is EMD method with which any complicated dataset can be decomposed into a finite number of Intrinsic Mode Functions(IMF).Using Hilbert transform to those IMF components can obtain meaningfulinstantaneous frequency, the final presentation of this results is anenergy-frequency-time distribution, designated as the Hilbert spectrum.Firstly, this paper discussed the definitions of instantaneous frequency andIMF, then the EMD algorithm was presented. After that, meanings in physics ofHilbert/Huang Transform spectrum and marginal spectrum have been analyzed.Based on these, two factors which influenced on the accuracy and speed ofEMD-phenomenon of mode fission in noise signal analysis by EMD and endeffect have been put forward. In order to eliminate phenomenon of modefission in random noise analysis by EMD, an adaptive wavelet thresholdde-noising algorithm based on white noise detection and 3σ rule was presented;then, in order to weaken the end effect in EMD algorithm, data extensiontechnologies have been proposed. Algorithms of neuron network based dataextension and mirror based extension technologies have been discussed,meanwhile their limitations have been pointed out, too. For this, an envelopeextremum extension algorithm has been presented. Simulation results show thatenvelope extremum extension is an efficient and excellent method to eliminateend effect.Secondly, the paper studied the capabilities of Hilbert/Huang spectrum.Compared to morlet wavelet spectrum and Wigner-Ville distribution, theoreticanalysis and simulation experiment results show that HHT spectrum has perfecttime-frequency concentration, eliminates the cross-time interference and hasgood time-frequency resolution characteristics.Lastly, time-frequency analytic method based on EMD is used to analyzetime-frequency characteristics of numerical results of classical nonlinearequation system and detect singular index to demonstrate the efficiency andsuperiority of this new time-frequency analytic method.