Hilbert Spectrum for Time-Domain Measurement Data and Its Application

H.M. Peng, P.C. Chang, F.R. Chang

Abstract: In this paper, a new method for analyzing the time domain data is introduced. As one knows, the time domain phase measurements are nonstationary and the differencing technique is usually adopted for generating stationary data. Thus, the analysis tools for stationary data are used in such case. On the other hand, some nonstationary data processing methods could be used directly to analyze measurements, and time-varying phenomena of data will be revealed through these methods. A new algorithm based on the concept of the instantaneous frequency is described in this paper. The strategy is described as the following two parts. First, the measurements are decomposed into components with meaningful instantaneous frequencies. For this purpose, some restriction conditions for decomposition from the local viewpoint are necessary. After the process, the Hilbert transform will be applied to every component and the data will be expressed in phasor form. Under this circumstance, we can represent the amplitude and the instantaneous frequency as functions of time in a three-dimensional plot. This frequency-time distribution of the amplitude is designated as the Hilbert amplitude spectrum, and the squared values of amplitude could be substituted for energy to produce the Hilbert energy spectrum just as well. To verify our algorithm, some simulations are performed. Based on the simulation results, the time-varying spectrum characteristic can be easily identified. Furthermore, different types of noise also can be discriminated by its Hilbert spectrum. Besides, the marginal spectrum of the Hilbert spectrum offers a measure of total amplitude or energy contribution from each frequency value, which is more meaningful than the Fourier spectrum for nonstationary data. Based on the spectrum information, the optimal weighting factors between different measurements will be further investigated.
Published in: Proceedings of the 34th Annual Precise Time and Time Interval Systems and Applications Meeting
December 3 - 5, 2002
Hyatt Regency Reston Town Center
Reston, Virginia
Pages: 501 - 510
Cite this article: Peng, H.M., Chang, P.C., Chang, F.R., "Hilbert Spectrum for Time-Domain Measurement Data and Its Application," Proceedings of the 34th Annual Precise Time and Time Interval Systems and Applications Meeting, Reston, Virginia, December 2002, pp. 501-510.
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