HHT ppt

1. Hilbert Huang Transform(HHT)&Empirical Mode Decomposition(EMD)

2. What is HHT??? An algorithm for analyzing the data obtained from non-linear and non stationary systems Decomposes signal into “Intrinsic Mode Functions” Obtains “Instantaneous frequency” (not used in our project)

3. Hilbert Huang Transform: Need 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. They are actually not suitable for nonlinear and non-stationary, the signals encountered in practical engineering.

4. Intrinsic Mode Functions(IMF) Formal Definition:Any function with the same number of extrema and zero crossings, with its envelopes being symmetric with respect to zero Counterpart to simple harmonic function Variable amplitude and frequency along the time axis

6. Two Steps of HHT: Empirical Mode Decomposition (Sifting) Hilbert Spectrum Analysis

7. Empirical Mode Decomposition:Assumptions Data consists of different simple intrinsic modes of oscillations Each simple mode (linear or non linear) represents a simple oscillations Oscillation will also be symmetric with respect to the local mean

8. Sifting Process Explained

15. Algorithm Between each successive pair of zero crossings, identify a local extremum in the test data. Connect all the local maxima by a cubic spline line as the upper envelope. Repeat the procedure for the local minima to produce the lower envelope. Continued…..

16. Sifting……..continued Calculate mean of the local and upper minima Subtract this mean from the data set Take h1 as data set and repeat above procedure till hi satisfies the criteria of IMF, say Ci We take Ri=X(t)-Ci and repeat the above steps to find further IMF using Ri as the data set. Finally Ri becomes monotonic function from which we no IMF can further be obtained.

17. Stoppage Criteria Limit on SDk S Number: The number of consecutive siftings when the numbers of zero-crossings and extrema are equal or at most differing by one.

18. Comparative Study

19. Advantages of EMD in Financial Prediction Reduction in noise More choices in training the neural network

20. Drawbacks Less Robust System Restricted use of time-series neural network Longer Computational Time

21. Related mathematical problems Adaptive data analysis methodology in general Nonlinear system identification methods Prediction problem for nonstationary processes Spline problems

22. References Introduction to the Hilbert Huang Transform and its related mathematical problems by Nordan E. Huang