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- 1. Hilbert Huang Transform(HHT)&Empirical Mode Decomposition(EMD)<br />
- 2. What is HHT???<br />An algorithm for analyzing the data obtained from non-linear and non stationary systems<br />Decomposes signal into “Intrinsic Mode Functions”<br />Obtains “Instantaneous frequency” (not used in our project)<br />
- 3. Hilbert Huang Transform: Need<br />Traditional methods, e.g. Fourier Integral Transform, Fast Fourier Transform (FFT) and Wavelet Transform have a strong priori assumption that the signals being processed should be linear and/or stationary.<br />They are actually not suitable for nonlinear and non-stationary, the signals encountered in practical engineering.<br />
- 4. Intrinsic Mode Functions(IMF)<br />Formal Definition:Any function with the same number of extrema and zero crossings, with its envelopes being symmetric with respect to zero<br />Counterpart to simple harmonic function<br />Variable amplitude and frequency along the time axis<br />
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- 6. Two Steps of HHT:<br />Empirical Mode Decomposition (Sifting)<br />Hilbert Spectrum Analysis<br />
- 7. Empirical Mode Decomposition:Assumptions<br />Data consists of different simple intrinsic modes of oscillations<br />Each simple mode (linear or non linear) represents a simple oscillations<br />Oscillation will also be symmetric with respect to the local mean<br />
- 8. Sifting Process Explained<br />
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- 15. Algorithm<br />Between each successive pair of zero crossings, identify a local extremum in the test data.<br />Connect all the local maxima by a cubic spline line as the upper envelope.<br />Repeat the procedure for the local minima to produce the lower envelope. Continued…..<br />
- 16. Sifting……..continued<br />Calculate mean of the local and upper minima<br />Subtract this mean from the data set<br />Take h1 as data set and repeat above procedure till hi satisfies the criteria of IMF, say Ci<br />We take Ri=X(t)-Ci and repeat the above steps to find further IMF using Ri as the data set.<br />Finally Ri becomes monotonic function from which we no IMF can further be obtained.<br />
- 17. Stoppage Criteria<br />Limit on SDk<br />S Number: The number of consecutive siftings when the numbers of zero-crossings and extrema are equal or at most differing by one. <br />
- 18. Comparative Study<br />
- 19. Advantages of EMD in Financial Prediction<br />Reduction in noise<br />More choices in training the neural network<br />
- 20. Drawbacks<br />Less Robust System<br />Restricted use of time-series neural network<br />Longer Computational Time<br />
- 21. Related mathematical problems<br />Adaptive data analysis methodology in general<br />Nonlinear system identification methods<br />Prediction problem for nonstationary processes<br />Spline problems<br />
- 22. References<br />Introduction to the Hilbert Huang Transform and its related mathematical problems by Nordan E. Huang<br />

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