• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.09a
• /
• pp.820-821
• /
• 2005

• Geophysics and Geophysical Exploration
• /
• v.14 no.1
• /
• pp.1-6
• /
• 2011

As a check on calibration and drift in each discrete sub-system of a commercial frequency-domain airborne electromagnetic system, we aim to use causality constraints alone to predict in-phase from wide-band quadrature data. There are several possible applications of the prediction of in-phase response from quadrature data including: (1) quality control on base level drift, calibration and phase checks; (2) prediction and validation of noise levels in in-phase from quadrature measurements and vice versa and in future; and (3) interpolation and extrapolation of sparsely sampled data enforcing causality and better frequency-domain-time-domain transformations. In practice, using tests on both synthetic and measured Resolve helicopter-borne electromagnetic frequency domain data, in-phase data points could be predicted using a scaled Hilbert transform with a standard deviation between 40 and 80 ppm. However, relative differences between base levels between flight could be resolved to better than 1 ppm, which allows an independent quality control check on the accuracy of drift corrections.

• Journal of IKEEE
• /
• v.18 no.2
• /
• pp.240-247
• /
• 2014

Intraocular pressure is measured after a cornea air puff by observing biomechanical properties such as thickness or displacement of the cornea. In this paper, we deal with a frequency domain analysis of corneal deformation in the air puff tonometry that is used to diagnose glaucoma or lasik. We distinguish the patient from the normal by measuring the oscillation frequency in the neighborhood of the central cornea section. A binary image was obtained from the video images, and cornea vertical oscillation profile was extracted from the difference between the vertical displacement data and the curve fitting. In terms of Fourier transform, a vibration frequency of 479.2Hz for the patient was obtained as well as more higher 702.8Hz for the normal due to stiffness. Hilbert-Huang transform's empirical mode decomposition generally describes local, nonlinear, and nonstationary data. After the data were decomposed into intrinsic mode functions, a spectrum and power were analysed. Finally, we confirm that the patient has 6 times more higher power ratio for the specific intrinsic mode function between the patient and the normal.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1555-1566
• /
• 2023

A Hilbert space operator A ∈ B(H) is a generalised n-projection, denoted A ∈ (G-n-P), if A^*n = A. (G-n-P)-operators A are normal operators with finitely countable spectra σ(A), subsets of the set $\{0\}\,{\cup}\,\{\sqrt[n+1]{1}\}.$ The Aluthge transform à of A ∈ B(H) may be (G - n - P) without A being (G - n - P). For doubly commuting operators A, B ∈ B(H) such that σ(AB) = σ(A)σ(B) and ${\parallel}A{\parallel}\,{\parallel}B{\parallel}\;{\leq}\;{\parallel}{\tilde{AB}}{\parallel},$ ${\tilde{AB}}\;{\in}\;(G\,-\,n\,-\,P)$ if and only if $A\;=\;{\parallel}{\tilde{A}}{\parallel}\,(A_{00}\,{\oplus}\,(A_0\,{\oplus}\,A_u))$ and $B\;=\;{\parallel}{\tilde{B}}{\parallel}\,(B_0\,{\oplus}\,B_u),$ where A₀₀ and B₀, and A₀ ⊕ A_u and B_u, doubly commute, A₀₀B₀ and A₀ are 2 nilpotent, A_u and B_u are unitaries, A^*n_u = A_u and B^*n_u = B_u. Furthermore, a necessary and sufficient condition for the operators αA, βB, αà and ${\beta}{\tilde{B}},\;{\alpha}\,=\,\frac{1}{{\parallel}{\tilde{A}}{\parallel}}$ and ${\beta}\,=\,\frac{1}{{\parallel}{\tilde{B}}{\parallel}},$ to be (G - n - P) is that A and B are spectrally normaloid at 0.

• Structural Engineering and Mechanics
• /
• v.14 no.4
• /
• pp.417-434
• /
• 2002

This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

• Nuclear Engineering and Technology
• /
• v.47 no.2
• /
• pp.219-225
• /
• 2015

In this paper, a three-dimensional model for the dynamic analysis of a flywheel based on the finite element method is presented. The static structure analysis for the model provides stress and strain distribution cloud charts. The modal analysis provides the basis of dynamic analysis due to its ability to obtain the natural frequencies and the vibration-made vectors of the first 10 orders. The results show the main faults are attrition and cracks, while also indicating the locations and patterns of faults. The harmonic response simulation was performed to gain the vibration response of the flywheel under operation. In this paper, we present a Hilbert-Huang transform (HHT) algorithm for flywheel vibration analysis. The simulation indicated that the proposed flywheel vibration signal analysis method performs well, which means that the method can lay the foundation for the detection and diagnosis in a reactor main coolant pump.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.11 no.2
• /
• pp.939-951
• /
• 2019

A novel empirical mode decomposition strategy based on Fourier transform and band-pass filter techniques, contributing to efficient instantaneous vibration analyses, is developed in this study. Two key improvements are proposed. The first is associated with the adoption of a band-pass filter technique for intrinsic mode function sifting. The primary characteristic of decomposed components is that their bandwidths do not overlap in the frequency domain. The second improvement concerns an attempt to design narrowband constraints as the essential requirements for intrinsic mode function to make it physically meaningful. Because all decomposed components are generated with respect to their intrinsic narrow bandwidth and strict sifting from high to low frequencies successively, they are orthogonal to each other and are thus suitable for an instantaneous frequency analysis. The direct Hilbert spectrum is employed to illustrate the instantaneous time-frequency-energy distribution. Commendable agreement between the illustrations of the proposed direct Hilbert spectrum and the traditional Fourier spectrum was observed. This method provides robust identifications of vibration modes embedded in vibration processes, deemed to be an efficient means to obtain valuable instantaneous information.

• Publications of The Korean Astronomical Society
• /
• v.30 no.2
• /
• pp.605-607
• /
• 2015

The development of time-frequency analysis techniques allow astronomers to successfully deal with the non-stationary time series that originate from unstable physical mechanisms. We applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), to two non-stationary phenomena: the superorbital modulation in the high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of the AGN RE J1034+396. From the analysis of SMC X-1, we obtained a Hilbert spectrum that shows more detailed information in both the time and frequency domains. Then, a phase-resolved analysis of both the spectra and the orbital profiles was presented. From the spectral analysis, we noticed that the iron line production is dominated by different regions of this binary system in different superorbital phases. Furthermore, a pre-eclipse dip lying at orbital phase ~0:6-0:85 was discovered during the superorbital transition state. We further applied the HHT to analyze the QPO of RE J1034+396. From the Hilbert spectrum and the O-C analysis results, we suggest that it is better to divide the evolution of the QPO into three epochs according to their different periodicities. The correlations between the QPO periods and corresponding fluxes were also different in these three epochs. The change in periodicity and the relationships could be interpreted as the change in oscillation mode based on the diskoseismology model.

• Journal of Biosystems Engineering
• /
• v.34 no.2
• /
• pp.127-132
• /
• 2009

In the working population, muscle fatigue and musculoskeletal discomfort are common, which, in the case of insufficient recovery may lead to musculoskeletal pain. Workers suffering from musculoskeletal pains need to be rehabilitated for recovery. Isokinetic testing has been used in physical strengthening, rehabilitation and post-operative orthopedic surgery. Frequency analysis of electromyography (EMG) signals using the mean frequency (MNF) has been widely used to characterize muscle fatigue. During isokinetic contractions, EMG signals present strong nonstationarities. Hilbert-Haung transform (HHT) and autoregressive (AR) model have been known more suitable than Fourier or wavelet transform for nonstationary signals. Moreover, several analyses have been performed within each active phase during isokinetic contractions. Thus, the aims of this study were i) to determine which one was better suitable for the analysis of MNF between HHT and AR model during repetitive maximum isokinetic extensions and ii) to investigate whether the analysis could be repeated for sequential fixed epoch lengths. Seven healthy volunteers (five males and two females) performed isokinetic knee extensions at $60^{\circ}/s$ and $240^{\circ}/s$ until 50% of the maximum peak torque was reached. Surface EMG signals were recorded from the rectus femoris of the right thigh. An algorithm detecting the onset and offset of EMG signals was applied to extract each active phase of the muscle. Following the results, slopes from the least-square error linear regression of MNF values showed that muscle fatigue of all subjects occurred. The AR model is better suited than HHT for estimating MNF from nonstationary EMG signals during isokinetic knee extensions. Moreover, the linear regression can be extracted from MNF values calculated by sequential fixed epoch lengths (p> 0.0I).

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.7 no.3
• /
• pp.121-125
• /
• 2014

A hardware implementation of Hilbert transform is indespensible element in DSP system, but it suffers form a high complexity of system level hardware resulted in a large amount of the used gate. In this paper, we implemented the Hilbert transformer using MAG algorithm that reduces the complexity of hardware.