Hilbert huang transform(hht)
Post on 24-May-2015
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Hilbert Huang Transform(HHT)&
Empirical Mode Decomposition(EMD)
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)
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.
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 functionVariable amplitude and frequency along the
time axis
Two Steps of HHT:
Empirical Mode Decomposition (Sifting)
Hilbert Spectrum Analysis
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
Sifting Process Explained
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…..
Sifting……..continuedCalculate mean of the local and upper
minimaSubtract 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.
Stoppage CriteriaLimit 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.
Comparative Study
Advantages of EMD in Financial Prediction
Reduction in noise
More choices in training the neural network
Drawbacks
Less Robust System
Restricted use of time-series neural network
Longer Computational Time
Related mathematical problemsAdaptive data analysis methodology in
general
Nonlinear system identification methods
Prediction problem for nonstationary
processes
Spline problems
References
Introduction to the Hilbert Huang Transform and its related mathematical problems by Nordan E. Huang
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