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Hilbert transform separation and analysis of multicomponent oscillations

1 March, 2012

Author: Michael Feldman
Source: 4th International Conference on Localization, Energy and Nonrmal Modes in Mechanics and Physics
Abstract: The objective of the paper is to demonstrate a Hilbert transform      (HT) method      for analysis of multicomponent vibration of mechanical systems      under free and      forced vibration regimes. The method is based on the HT of      input/output signals      in a time domain to separate nonstationary vibration components      and extract the      instantaneous dynamic structure characteristics those as natural      frequencies, stiffness,      damping, and their variations in time. The HT rather assigns a      complementary      imaginary part to a given real signal part, or vice versa, by      shifting each      component of the signal by a quarter of period. Thus, the HT pair      provides a      method for determining the instantaneous amplitude and the      instantaneous      frequency of a signal. For the general non-stationary vibration      signal the      analytic signal method do a better job of simultaneously      time-frequency      localizing of the main signal components. The analytic signal      method is equally      applicable to deterministic and random processes, although,      generally speaking,      it doesn’t divide them into two separate groups.