• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.383-387
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• 2002

Let p be an odd prime, and let f($\varkappa$) be the interpolating polynomial associated with a table of data points (j+1, (equation omitted) ) for 0$\leq$j$\leq$p. In this article, we find congruence identities modulo p of (p-1)!f($\varkappa$), (p-2)!f($\varkappa$), and (p-3)!f($\varkappa$). Moreover we present some conjectures of these types.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2277-2279
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. This paper presents the method for improving the accuracy of the Block Pulse series coefficients and derives the related integration operational matrices by using the Lagrange second order interpolation polynomial and expands that matrix to general form.

• Journal of Korean Society for Geospatial Information Science
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• v.14 no.4 s.38
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• pp.27-36
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• 2006

Conventionally, in order to get accurate geolocation of satellite images we need a set of ground control points with respect to individual scenes. In this paper, we tested the possibilities of modeling satellite orbits from individual scenes by establishing a sensor model for one scene and by applying the model, which was derived from the same orbital segment, to other scenes that has been acquired from the same orbital segment. We investigated orbit-attitude models with several interpolation methods and with various parameter sets to be adjusted. We used 7 satellite images of SPOT-3 with a length of 420km and ground control points acquired from GPS surveying. Results of the conventional individual scene modeling hardly introduced differences among different interpolation methods and different adjustment parameter sets. As the results of orbit modeling, the best model was the one with Lagrange interpolation for position/velocity and linear interpolation for attitude and with position/angle bias as parameter sets. The best model showed that it is possible to model orbital segments of 420km with ground control points measured within one scene (60km).

• Journal of information and communication convergence engineering
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• v.13 no.4
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• pp.235-240
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• 2015

A decimation chain for multi-standard reconfigurable radios is presented for 900-MHz and 1,900-MHz dual-band cellular standards with a data interpolator based on the Lagrange method for adjusting the variable data rate to a fixed data rate appropriate for each standard. The two proposed configurations are analyzed and compared to provide insight into aliasing and the signal bandwidth by means of a newly introduced measure called interpolation error. The average interpolation error is reduced as the ratio of the sampling frequency to the signal BW is increased. The decimation chain and the multi-rate analog-to-digital converter are simulated to compute the interpolation error and the output signal-to-noise ratio. Further, a method to operate the above-mentioned chain under a compressed mode of operation is proposed in order to guarantee continuous packet connectivity for inter-radio-access technologies. The presented decimation chain can be applied to LTE, WCDMA, GSM multi-mode multi-band digital front-end which will ultimately lead to the software-defined radio.

• Proceedings of the KOSOMBE Conference
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• v.1997 no.11
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• pp.459-463
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• 1997

In this paper, we present the elimination of ECG artifact from the polysomnographic EEG and EOG. The idea of this method is that the ECG synchronized EEG segment is detected from ECG and regard samples of that segment a missing signal. After this, we used two interpolation methods to recover the missing segment. One is the Lagrange Polynomial Interpolation Method and the other is the Least Square Error AR Interpolation method. We tested those methods by applying to simulated signals. AR methods works well enough to reject the artifact about 10% of the main artifact level. We practically applied to real EEG and EOG signals. We also developed the algorithm to detect whether the artifact level is high or not. If the artifact level is high, then the interpolations are applied.

• Magazine of the Korean Society of Agricultural Engineers
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• v.40 no.3
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• pp.103-112
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• 1998

In this study, database schema which is capable of maintaining various design-knowledge and applicable to the structural designs has been presented. Futhermore, by utilizing the database system, RECODSS (REinforced COncrete Design Support System) was developed as well. Knowledge-base that were formulated from the document is constructed by applying the concrete standard specifications of Korea from 1989. The basic drawing was prepared by $AutoCAD^TM$. As an inference in the preliminary design, the certainty function and the interpolation function were presented. The certainty function is made by assuming linear relations between each data while referencing $MYCIN^TM$ (expert systems). Nevertheless, the interpolation function was made by utilizing the linear Lagrange interpolation. For the search of the design-knowledge, fast search algorithm and full-text search algorithm were used, however, the design engine was programmed with C language. RECODSS was applied for designing a slab and a beam member. And the results were compared with the existing results. In conclusion, RECODSS was able to efficiently manage various design knowledge and to introduce stable design results.

• Journal of the Korean Institute of Gas
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• v.18 no.3
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• pp.1-12
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• 2014

In this paper, we developed an explosion proof type and portable combustible gas leak detector and proposed an algorithm to improve the accuracy for measuring gaseous concentrations. The nation's first we developed an infrared gas leak detector with explosion proof standard(Ex d ib) and improved measuring accuracy by using linearization recursion equation and 2nd Lagrange interpolation polynomial. Together, we advanced their performances and added their easy functions after investigating field demands. To compare our and other company's detectors, we performed measurement tests with eight standard gases made by Korea Gas Safety Corporation. We demonstrated the excellence of our instruments in measuring accuracy other than detecters through experimental results.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.2
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• pp.245-250
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• 2014

This paper introduces the inverse synthetic aperture radar(ISAR) imaging technique for rear view target of an automobile, which uses both linear frequency modulation-frequency shift keying(LFM-FSK) waveform and monopulse tracking. LFM-FSK waveform consists of two sequential stepped frequency waveforms with some frequency offset, and thus, can be used to generate ISAR images of rear view target of an automobile. However, ISAR images can often be blurred due to non-uniform change rate of relative aspect angle between radar and target. In order to address this problem, one-dimensional(1-D) Lagrange interpolation technique in conjunction with angle information obtained from the monopulse tracking is applied to generate uniform data across the radar's aspect angle. Simulation results show that the proposed method can provide focused ISAR images.

• JSTS:Journal of Semiconductor Technology and Science
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• v.14 no.1
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• pp.109-116
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• 2014

This paper presents a high-efficiency digital class-D audio amplifier using a composite interpolation filter for portable audio devices. The proposed audio amplifier is composed of an interpolation filter, a delta-sigma modulator, and a class-D output stage. To reduce power consumption, the designed interpolation filter has an optimized composite structure that uses a direct-form symmetric and Lagrange FIR filters. Compared to the filters with homogeneous structures, the hardware cost and complexity are reduced by about half by the optimization. The coefficients of the digital delta-sigma modulator are also optimized for low power consumption. The class-D output stage has gate driver circuits to reduce shoot-through current. The implemented class-D audio amplifier exhibited a high efficiency of 87.8 % with an output power of 57 mW at a load impedance of $16{\Omega}$ and a power supply voltage of 1.8 V. An outstanding signal-to-noise ratio of 90 dB and a total harmonic distortion plus noise of 0.03 % are achieved for a single-tone input signal with a frequency of 1 kHz.