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As for me, the most interesting and curious is adaptive signal processing.
I have been working for 2 years with EMD (Empirical mode decomposition) and SSA (Singular spectrum analysis) and I've got great results.
These methods of adaptive signal processing mean extracting the basis functins (IMF in EMD and EOFs in SSA ) just from the processed data, without applying any other functions. The constructed basis allows to hold denoising, detrending, extrapolation and statistical analysis of signals. Besides, you get time-frequency distributions (Hilbert-Huang colored map in EMD) which depict all the events in signal on time-frequency plane. It's possible to find out signal modulations (time and frequency), domains of energy concentration, define marginal spectrum, instantaneous energy density and measure of stationarity
Recently I've introduced the technique of solving Data Mining problems with EMD. These includes clustering, segmentation, classification and etc.
If my suggestion is interesting for you, write me as soon as possible. I have many articles and books in pdf, Matlab codes.
EMD - is a conception based on representation of the signal by a finite number of special functions, called IMFs (intrinsic mode functions), which reflect the internal structure and local features of the studied process. Obtained just from the signal, IMFs must satisfy 2 necessary conditions :
1) The total number of extrema and zero-crossings on the whole duration of the signal must be equal or differ at most by one.
2) The average of 2 envelopes - upper envelope, which interpolates local maxima and lower envelope, which interpolates local minima, must be close to zero (the accuracy usually depends on the concrete task).
Among numerous methods of interpolation cubic splines are often used because of the high degree of their smoothness and small oscillation effect. If the signal is limited in time domain (has finite number of samples and en-ergy) and possesses at least 1 maxima and 1 minima it can always be decomposed into a set of IMFs. The approximate number of IMFs is expressed by the following empiric formula:
K=]logN[+(-)1
where N- number of discrete samples, ][- mathematical operation of rounding to the nearest integer towards minus infinity ( ).
If extrema are absent, signal may be differentiated once or more in order to reveal at least one. Afterwards, when the algorithm is finished, return to initial set of values is made.
EMD has 4 main modifications: global, local, online and fast decompositions.
Among the fundamental properties are adap-tivity, fullness, completeness and orthogonality. The frequency properties of IMFs provide new interpretation of EMD as a dyadic filter bank, which comprises the collection of filters with overlapping on frequency band. The effective width of the corresponding frequency characteristic decreases with increase of the IMF number. Restoration of the signal is made according to the following formula:
s(t) = sum (ci(t)) + r(t)
where {ci(t)}i=1,N - extracted IMFs, r(t)- final residual (constant or trend), which can't be further decomposed at all.
EMD is widely used in various proce-dures of the so-called initial signal processing . These procedures include adaptive denoising and classification of the extracted noise according to the Hurst's parameter, allocation and exception of trend (detrending), extrapolation and statistical analysis. Very important and significant is time-energy-frequency Hilbert-Huang representation, computed on the base of application of Hilbert transform to the IMFs. This 3-dimensional colored map depicts amplitude and frequency modulations in signal, identifies time and fre-quency domains of energy concentration. It also paves the way to defining marginal spectrum and instantaneous energy density, which are much more convenient for nonlinear and non-stationary signals than their Fourier sub-stitutions. Finally, Hilbert spectrum avoids the negative influence of Heisenberg's uncertainty principle, which maintains that the process can't be simultaneously localized in time and frequency domains.
If this topic is interesting, please, write. I'll be happy to answer the questions.
hi sir i want to know whether any projects related to the above mentioned topic(EMD) are ready with u.i'm in a urgent need of that and awaiting ur reply.
Well, I remember my promise, don't be worried. Now I really have lack of time because of preparation for the WorkShop in Germany next week. Nevertheless, I'll try to send you EMD papers and files as soon as possible!!!!
I'm working with Adaptive signal processing. It sounds very interesting your research about EMD and SSA. I would really appreciate if your share all this information with us.
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