• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1209-1219
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• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

• Journal of information and communication convergence engineering
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• v.14 no.2
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• pp.78-83
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• 2016

In underwater acoustic communication, the transmitted signals are severely influenced by the reflections from both the sea surface and the sea bottom. As very large reflection signals from these boundaries cause an inter-symbol interference (ISI) effect, the communication quality worsens. A channel estimation-based equalizer is usually adopted to compensate for the reflected signals under the acoustic communication channel. In this study, a feed-forward equalizer (FFE) with the least mean squares (LMS) algorithm was applied to a quadrature phase-shift keying (QPSK) transmission system. Two different types of equalizers were adopted in the QPSK system, namely a real-coefficient equalizer and a complex-coefficient equalizer. The performance of the complex-coefficient equalizer was better than that of two real-coefficient equalizers. Therefore, a Hilbert transform was applied to the real-coefficient binary phase-shift keying (BPSK) system to obtain a complex-coefficient BPSK system. Consequently, we obtained better results than those of a real-coefficient equalizer.

• Journal of Electrical Engineering and Technology
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• v.10 no.5
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• pp.2126-2134
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• 2015

The present study suggests a localization method for the first (S₁) and the second (S₂) feature of heart sounds, based on an algorithm involving frequency filtering, energy detection, and interval regulation. Localization accuracy was evaluated by comparing the algorithm with the traditional Hilbert transform-based localization method. Results show that the sensitivity and the positive predictivity value of proposed method, respectively, were 97.27 % and 99.94 % in S₁ detection and 94.99 % and 100 % in S₂ detection.

• Computers and Concrete
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• v.20 no.5
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• pp.521-527
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• 2017

This paper proposes using the multi-type sensor vibration measurements, such as from a relative displacement sensors and a traditional accelerometer for the damage detection of shear connectors in composite bridge under moving loads. Hilbert-Huang Transform (HHT) spectra of these responses will be fused with a data fusion approach i.e., Dempster-Shafer method, to detect the damage of shear connectors. Experimental studies on a composite bridge model in the laboratory are conducted to demonstrate the effectiveness and performance of using the proposed approach in detecting the damage of shear connectors in composite bridges. Both undamaged and damaged scenarios are considered. The detection results with the data fusion of multi-type sensor measurements show a more reliable and robust performance and accuracy, avoiding the false identifications.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.298-299
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• 2014

The solution of transient response of complex stiffness system was obtained using a green function of this system. To derive the green function, governing equation of this systems was expressed in Steady Space and solved by the diagonalization. The solution of this system are written as a convolution integral form. The result that are calculated by the numerical integration process for transient responses was showed properly.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.93-100
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• 2008

Recently, due to the advanced measurement techniques, long-term health monitoring systems have been frequently applied to existing bridges. It is known that damping ratios as one of dynamic properties would be an important parameter for evaluating the bridge condition. However, damping ratios may be normally varied depending on the external loading effects on bridges. In general, both the logarithmic decrement and the half-power band width method as a conventional method can be simply used for evaluating the damping ratios accurately when bridge response signals are measured under free vibration conditions. In this study, the Hilbert-Huang transform and the extended Kalman filter were applied to evaluate the damping ratio by using the bridge acceleration signals measured under ambient vibration condition. From the results under ambient vibration condition of bridges, it was examined that the damping ratios evaluated from both the Hilbert-Huang transform and the extended Kalman filter could be more reliable than those from conventional methods.

• Journal of the Korea Institute of Military Science and Technology
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• v.10 no.2
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• pp.12-20
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• 2007

The aiming ability is a key to improve the accuracy performance of the gun pointing system in the ground military vehicle. This paper describes the new detection method of chatter vibration using disturbance acceleration in the pointing structure. In order to analysis the vibration trends of the pointing system occurred while the vehicle driving, acceleration data obtained from vehicle was processed by using data processing algorithm with moving average and Hilbert transform. The specific mode constants of acceleration were obtained from various disturbances. Vehicle velocity, road condition and property of pointing structure were considered as factors which make the change of vibration trend in vehicle dynamics. Finally, back propagation neural networks have been applied to the pattern recognition of the classification of vibration signal in various driving conditions. Results of signal processing were compared with other condition result and analysed.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.7
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• pp.364-369
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• 2004

In this Paper, a flashover prediction method using the leakage current in the contaminated EPDM distribution polymer insulator is proposed. The leakage currents on the insulator were measured simultaneously with the different salt fog application such as 25g, 50g, and 75g per liter of deionized water. Then, the measured leakage currents were enveloped and transformed as the CDFS using the Hilbert transform and the level crossing rate, respectively. The obtained CDFS having different gradients(angles) were used as a important factor for the flashover prediction of the contaminated polymer insulator. Thus, the average angle change with an identical salt fog concentration was within a range of 20 degrees, and the average angle change among the different salt fog concentrations was 5 degrees. However, it is hard to be distinguished each other because the gradient differences among the CDFS were very small. So, the new weighting value was defined and used to solve this problem. Through simulation, it Is verified that the proposed method has the capability of the flashover prediction.

• Journal of The Korean Astronomical Society
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• v.56 no.1
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• pp.125-135
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• 2023

Here, we investigated the observed sunspot areas with respect to latitudes using the Hilbert transform technique. Conventional study of the cyclic patterns of sunspots is based on the Lomb-Scargle periodogram, which only obtains the amplitude information. In comparison, our approach characterizes the amplitude as well as the phase of solar activity. We demonstrated the solar North-South asymmetry in the instantaneous amplitude by analyzing daily sunspot data set spanning from the solar cycles 11 to 24. Our findings confirm that the northern hemisphere is dominant in the solar cycles 14, 15, 16, 18, and 20. Unlike the amplitude, the North-South asymmetry in the period of solar activity could not be established. We have also found that the standard deviation as a measure of fluctuation in the phase derivative is minimum in the latitude band 10° < l < 20°, and the fluctuations obtained for latitudes above 30° are considerable.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1575-1581
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• 2003

As a society has progressed rapidly toward a highly advanced digital information age, a multimedia communication service for acquisition, transmission and storage of image data as well as voice has being commercialized externally and internally. However, in the process of digitalization or transmission of data, noise is generated by several causes, and researches for eliminating those noises have been continued until now. There were the existing FFT(fast fourier transform) and STFT(short time fourier transform) for removing noise but it's impossible to know information about time and time-frequency localization capabilities has conflictive relationship. Therefore, for overcoming these limits, wavelet transform which is presented as a new technique of signal processing field is being applied in many fields recently. Because it has time-frequency localization capabilities it's Possible for multiresolution analysis as well as easy to analyze various signal. And when two wavelet base were designed to form Hilbert transform pair, wavelet pair provide superior performance than the existing DWT(discrete wavelet transform) in data characteristic detection. Therefore in this parer, we removed impulse noise by using adaptive-length median filter and two dyadic wavelet base which is designed by truncated coefficient vector.