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**Nonlinear time-varying spectral analysis: HHT and MODWPT.**
*(English)*
Zbl 1192.65087

Summary: The time-frequency distribution has received a growing utilization for analysis and interpretation of nonlinear and nonstationary processes in a variety of fields. Among them, two methods, such as, the empirical mode decomposition (EMD) with Hilbert transform (HT) which is termed as the Hilbert-Huang Transform (HHT) and the Hilbert spectrum based on the maximal overlap discrete wavelet package transform (MODWPT), are fairly noteworthy. Comparisons of HHT and MODWPT in analyzing several typical nonlinear systems and examinations of the effectiveness using these two methods are illustrated. This study demonstrates that HHT can provide comparatively more accurate identifications of nonlinear systems than MODWPT.

### MSC:

65K10 | Numerical optimization and variational techniques |

93B30 | System identification |

93E12 | Identification in stochastic control theory |

65T60 | Numerical methods for wavelets |

### Keywords:

empirical mode decomposition; Hilbert transform; Hilbert-Huang transform; Hilbert spectrum; maximal overlap discrete wavelet package transform; identifications of nonlinear systems
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\textit{P.-W. Shan} and \textit{M. Li}, Math. Probl. Eng. 2010, Article ID 618231, 14 p. (2010; Zbl 1192.65087)

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