• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.495-517
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• 2022

Let M_α be a bilinear fractional maximal operator and BM_α be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators M^j_α,β and BM^j_α,β (j = 1, 2), the fractional maximal iterated commutator ${\mathcal{M}}_{{\alpha},{\vec{b}}}$, and $BM_{{\alpha},{\vec{b}}}$, where b ∈ BMO(ℝ^d) and ${\vec{b}}\;=\;(b_1,b_2)\;{\in}\;BMO({\mathbb{R}}^d)\;{\times}\;BMO({\mathbb{R}}^d)$. In particular, we improve the well-known results to a larger scale for 1/2 < q < ∞ and give positive answers to the questions in [2].

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.545-551
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• 1996

It is well known in the theory of distributions and proved in [GS, S] that $$ (i) (Bochner-Schwartz) Every positive definite (tempered) distribution is the Fourier transform of a positive tempered measure \mu. $$ $$ (ii) (Schwartz kernel theorem) Let B(\varphi, \psi) be a bilinear distribution. Then for some u \in D'(R^n \times R^n) B(\varphi, \psi) = u(\varphi(x)\bar{\psi}(y)) for every \varphi, \psi \in C_c^\infty. $$ $$ (iii) A translation invariant positive definite bilinear distribution B(\varphi, \psi) is of the form B(\varphi, \psi) = \smallint \varphi(x)\psi(x) d\mu(x) for every \varphi, \psi \in C_c^\infty (R^n), where \mu is a positive tempered measure.

• International Journal of Contents
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• v.6 no.4
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• pp.1-7
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• 2010

Natural images often contain useful information about the scene such as text or company logos placed on a rectangular shaped plane. The 2D images captured from such objects by a camera are often distorted, because of the effects of the perspective projection camera model. This distortion makes the acquisition of the text information difficult. In this study, we detect the rectangular object on which the text is written, then the image is restored by removing the perspective distortion. The Hough transform is used to detect the boundary lines of the rectangular object and a bilinear transformation is applied to restore the original image.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.5
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• pp.808-815
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• 1990

This paper treats with the design method for the single loop oversampled Sigma-Delta A/D converter with one delay and the digital integrator. Such an integrator was kgenerated by means of the bilinear transform of the analog integrator. The frequency spectrums of the quantizer and the decimator output signal are evaluated by FFT respectively. With the performance evaluation system, the values of SNR are obtained versus the input sinusoidal signal amplitude, frequency, the oversampling ratio, the DC-input level, the loop gain and the limitting value of the integrator. As compared with existing results, values of SNR versus the input signal amplitude and the oversampling ratio for the suggested system are about 6dB higher then previously reported results respectively. Furthermore, this approach achieves an about 60dB input dynamic range.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.10a
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• pp.227-232
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• 1995

This paper presents a digital modeling technique for the distributed parameter system. The basic idea of the proposed technique is to discretize a continuous system with respect to the spatial coordinate using the approximate methods such as bilinear method and backward difference method. The response of the discretized system is analyzed by Laplace transform and Z transform. The computational result of the proposed technique in a torsional shaft is compared with the exact solution and the result of the finite element method.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2411-2413
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• 1998

In this paper, using tile concept of block digital filtering, and the design procedure of time-interleaved oversampling converter are presented. it is shown that arbitrary sigma-delta A/D converter can be converted into corresponding time-interleaved structure. The TIM structure of this paper is designed by the bilinear transform. To verify the simulation results, a second-order TIM structure A/D converter has been implemented and the design process as well as experimented results are presented.

• Progress in Medical Physics
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• v.11 no.1
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• pp.39-47
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• 2000

In Stereotactic Radiosurgery (SRS), there are three imaging methods of target localization, such as digital subtraction Angiography (DSA), computed tomography (CT), magnetic resonance imaging (MRI). Especially, DSA and MR images have a distortion effect generated by each modality. In this research, image properties of DSA were studied. A first essential condition in SRS is an accurate information of target locations, since high dose used to treat a patient may give a complication on critical organ and normal tissue. Hut previous localization program did not consider distortion effect which was caused by image intensifier (II) of DSA. A neurosurgeon could not have an accurate information of target locations to operate a patient. In this research, through distortion correction, we tried to calculate accurate target locations. We made a grid phantom to correct distortion, and a target phantom to evaluate localization algorithm. The grid phantom was set on the front of II, and DSA images were obtained. Distortion correction methods consist of two parts: 1. Bilinear transform for geometrical correction and bilinear interpolation for gray level correction. 2. Automatic detection method for calculating locations of grid crosses, fiducial markers, and target balls. Distortion was corrected by applying bilinear transform and bilinear interpolation to anterior-posterior and left-right image, and locations of target and fiducial markers were calculated by the program developed in this study. Localization errors were estimated by comparing target locations calculated in DSA images with absolute locations of target phantom. In the result, the error in average with and without distortion correction is $\pm$0.34 mm and $\pm$0.41 mm respectively. In conclusion, it could be verified that our localization algorithm has an improved accuracy and acceptability to patient treatment.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.291-297
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• 2012

Conventional Fourier analysis can give only limited information about the dynamic characteristics of nonstationary signals. Instead, time-frequency analysis is widely used to investigate the nonstationary signal in detail. Several time-frequency analysis methods are compared for a typical acoustic emission burst generated during the impact between a ferrite ceramic and aluminum plate. This AE burst is inherently nonstationary and random containing many frequency contents, which leads to severe interference between cross terms in bilinear convolution type distributions. The smoothing and reassignment processes can improve the readability and resolution of the results. Spectrogram and scalogram of the AE burst are obtained and compared to get the characteristics information. Renyi entropies are computed for various bilinear time-frequency transforms to evaluate the randomness. These bilinear transforms are reassigned by using the improved algorithm in discrete computation.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.157-160
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• 1996

Physical systems axe generally continuous-time in nature. However as the data measured from these systems is generally in the form of discrete samples, and most modern signal processing is performed in the discrete-time domain, discrete-time models are employed. This paper describes methods for estimating the coefficients of continuous-time system within a closed loop control system. The method employs a recursive estimation algorithm to identify the coefficients of a discrete-time bilinear-operator model. The coefficients of the discrete-time bilinear-operator model closely approximate those of the corresponding continuous-time Laplace transform transfer function.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.4 no.1
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• pp.25-31
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• 1979

All the resitors in the active RC filter networks can be relplaced by the switched capacitors. Therefore, An SC filter circuit can be fully integrated using MOS technology. A switched capacitor is much better than a resistor in temperature and linearity characteristics, and the former can be fabricated on the much smaller area then the latter. In this paper, It is given the generalized disign method of the active SC filter from the active RC filter using Bilinear Z-transformation. By SC filtering Techniques using Bilinear Z-transform, It enalbes us to realize the FDNR and Gyrator filters, which could not be realized in the exsisting designs, and it permits the processing of signals at much higher frequenies that many previous designs do. Experiments show that the response of the SC active filter is similiar to that of its prototype active RC filter.