Hilbert-Huang Transform Analysis of Hydrological and by A.R. Rao, E.-C. Hsu

By A.R. Rao, E.-C. Hsu

The Hilbert-Huang remodel ((HHT) is a lately constructed strategy that's used to investigate nonstationary facts. Hydrologic and environmental sequence are, in most cases, analyzed through the use of innovations that have been constructed for desk bound information. This has resulted in difficulties of interpretation of the consequences. Environmental and hydrologic sequence are normally nonstationary. the elemental goal of the fabric mentioned during this publication is to investigate those information by utilizing tools in accordance with the Hilbert-Huang rework. those effects are in comparison to the consequences from the conventional equipment reminiscent of these in response to Fourier remodel and different classical statistical checks.

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4 A Signal with Three Close Frequencies A simple harmonic wave (Eq. 05 cycles/second is considered here. 7. 3) The IMF represents simple oscillation modes embedded in the signal with zero mean. However, with this example, a problem is discovered. 7, we can see the first mode, c1 , actually involves these frequencies of oscillations together and cannot be successfully separated. The reason for this situation is because an IMF is not restricted to a narrow band signal; it can be both frequency and amplitude modulated as in c1 .

1 are used for simulation. 8. Since the overall amplitudes vary with each simulation as well as the phase, the simulated data have higher variability compared to those generated by using only random phase values. From the results of method 2 presented in Fig. 8, the variation of the simulated data is much higher than the results from method 1. 1. 1. 1. 2. Comparison of characteristics of five simulated series for HCN 120177 monthly rainfall data by method 1. 3. 4. 5. 6. 7. 8. 8.

X t is a random process. One can generate the random phase angles and recombine the IMFs. Due to the central limit theorem, X t approaches a Gaussian process for large n. This method is easy to implement. aj t , j t and rn t are obtained by the empirical mode decomposition, so j is the only generated variable and it does not vary with time. 13. (a) The theoretical power spectrum of AR(2) model; (b) the HHT marginal spectrum obtained from the first two IMF components (c1 and c2 ); (c) the Fourier spectrum and (d) the Multi-Taper method spectrum.

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