• Journal of Astronomy and Space Sciences
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• v.30 no.2
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• pp.79-82
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• 2013

We present the Hilbert-Huang transform (HHT) analysis on the quasi-periodic modulation of SMC X-1. SMC X-1, consisting of a neutron star and a massive companion, exhibits superorbital modulation with a period varying between ~40 d and ~65 d. We applied the HHT on the light curve observed by the All-Sky Monitor onboard Rossi X-ray Timing Explorer (RXTE) to obtain the instantaneous frequency of the superorbital modulation of SMC X-1. The resultant Hilbert spectrum is consistent with the dynamic power spectrum while it shows more detailed information in both the time and frequency domains. According to the instantaneous frequency, we found a correlation between the superorbital period and the modulation amplitude. Combining the spectral observation made by the Proportional Counter Array onboard RXTE and the superorbital phase derived in the HHT, we performed a superorbital phase-resolved spectral analysis of SMC X-1. An analysis of the spectral parameters versus the orbital phase for different superorbital states revealed that the diversity of $n_H$ has an orbital dependence. Furthermore, we obtained the variation in the eclipse profiles by folding the All Sky Monitor light curve with orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip of Her X-1, can be observed only in the superorbital ascending and descending states, while the width is anti-correlated with the X-ray flux.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.9
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• pp.3087-3103
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• 2022

Nearest neighbor query in location-based services has become a popular application. Aiming at the shortcomings of the privacy protection algorithms of traditional ciphertext nearest neighbor query having the high system overhead because of the usage of the double Hilbert curves and having the inaccurate query results in some special circumstances, a privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve has been proposed. This algorithm uses a single Hilbert curve to transform the two-dimensional coordinates of the points of interest into Hilbert values, and then encrypts them by the order preserving encryption scheme to obtain the one-dimensional ciphertext data which can be compared in numerical size. Then stores the points of interest as elements composed of index value and the ciphertext of the other information about the points of interest on the server-side database. When the user needs to use the nearest neighbor query, firstly calls the approximate nearest neighbor query algorithm proposed in this paper to query on the server-side database, and then obtains the approximate nearest neighbor query results. After that, the accurate nearest neighbor query result can be obtained by calling the precision processing algorithm proposed in this paper. The experimental results show that this privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve is not only feasible, but also optimizes the system overhead and the accuracy of ciphertext nearest neighbor query result.

• Kyungpook Mathematical Journal
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• v.9 no.1_2
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• pp.71-75
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• 1969

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.317-325
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• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.414-419
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• 2003

There are some methods fur extracting mode shapes from a continuously scanned data such as a modulation, Chebyshev polynomial, and Hilbert approach. In this paper, Chebyshev and Hilbert approaches were investigated through the numerical experiment first. As some experimental parameters were altered with small quantities, data were checked and plotted. From those results, the effects of unexpected parameters will be configured. And then, it will be actually helpful to select the proper method for specific testing environments.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.03a
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• pp.159-168
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• 2002

A recently developed filbert-Huang transform (HHT) technique is applied to detect damage locations of bridge structures. The HHT may be used to identify the locations of damages which exhibit nonlinear and nonstationary behavior, since the HHT can show the instantaneous frequency characteristics of the signal. A series of numerical simulations were conducted for bridge pier systems with damages under a controlled load with sweeping frequency. The results of the numerical simulation study indicate that the HHT method can reasonably identify damage locations using a limited number of acceleration sensors under severe measurement noise condition.

• Smart Structures and Systems
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• v.16 no.5
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• pp.919-935
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• 2015

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD has been successfully applied for identification of mode shapes of structures based on input-output approaches. This paper aims to extend application of EMD for output-only identification of mode shapes of linear structures. In this regard, a new simple and efficient method based on band-pass filtering and EMD is proposed. Having rather accurate estimates of modal frequencies from measured responses, the proposed method is capable to extract the corresponding mode shapes. In order to evaluate the accuracy and performance of the proposed identification method, two case studies are considered. In the first case, the performance of the method is validated through the analysis of simulated responses obtained from an analytical structural model with known dynamical properties. The low-amplitude responses recorded from the UCLA Factor Building during the 2004 Parkfield earthquake are used in the second case to identify the first three mode shapes of the building in three different directions. The results demonstrate the remarkable ability of the proposed method in correct estimation of mode shapes of the linear structures based on rather accurate modal frequencies.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.2
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• pp.179-190
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• 2017

Hand Accelerometers are widely used to detect human motion patterns in real-time. It is essential to reliably identify which type of activity is performed by human subjects. This rests on having accurate template of each activity. Many human activities are represented as a set of multiple time-series data from such sensors, which are mostly non-stationary and non-linear in nature. This requires a method which can effectively extract patterns from non-stationary and non-linear data. To achieve such a goal, we propose the method to apply Hilbert-Huang Transform which is known to be an effective way of extracting non-stationary and non-linear components from time-series data. It is applied on samples of accelerometer data to determine its effectiveness.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.2
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• pp.112-119
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• 2007

In order to predict vibration trends occurred during vehicle drive, acceleration data was processed by using data processing algorithm with moving average and Hilbert transform. Specific mode constants of acceleration were obtained under various disturbance. Vehicle velocity, road condition, property of pointing structure were considered as factors which make change of vibration trend in vehicle dynamics. Results of signal processing were compared and analysed. Advanced performance of the timing selection algorithm from this study was verified by using simple equipment comparing with the deflection measurement laser system(Muzzle Reference System).