Hilbert huang transform(hht)
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Hilbert Huang Transform (HHT) and Empirical Mode Decomposition (EMD) are algorithms for analyzing data from non-linear and non-stationary systems. EMD decomposes signals into Intrinsic Mode Functions (IMFs) through a process called sifting. The sifting process identifies local extrema and decomposes the signal into IMFs until a monotonic residual function remains. HHT then applies the Hilbert transform to each IMF to obtain the instantaneous frequency. While traditional methods assume linearity and stationarity, HHT is suitable for real-world non-linear and non-stationary signals through the EMD sifting process.
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Hilbert huang transform(hht)
- 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 systemsDecomposes signal into “Intrinsic Mode Functions”Obtains “Instantaneous frequency” (not used in our project)
- 3. Hilbert Huang Transform: NeedTraditional 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 zeroCounterpart to simple harmonic functionVariable amplitude and frequency along the time axis
- 6. Two Steps of HHT:Empirical Mode Decomposition (Sifting)Hilbert Spectrum Analysis
- 7. Empirical Mode Decomposition:AssumptionsData consists of different simple intrinsic modes of oscillationsEach simple mode (linear or non linear) represents a simple oscillationsOscillation will also be symmetric with respect to the local mean
- 15. AlgorithmBetween 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……..continuedCalculate mean of the local and upper minimaSubtract this mean from the data setTake h1 as data set and repeat above procedure till hi satisfies the criteria of IMF, say CiWe 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 CriteriaLimit on SDkS Number: The number of consecutive siftings when the numbers of zero-crossings and extrema are equal or at most differing by one.
- 19. Advantages of EMD in Financial PredictionReduction in noiseMore choices in training the neural network
- 20. DrawbacksLess Robust SystemRestricted use of time-series neural networkLonger Computational Time
- 21. Related mathematical problemsAdaptive data analysis methodology in generalNonlinear system identification methodsPrediction problem for nonstationary processesSpline problems
- 22. ReferencesIntroduction to the Hilbert Huang Transform and its related mathematical problems by Nordan E. Huang