• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.779-787
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• 2017

Let m be the Lebesgue measure on ${\mathbb{C}}$ normalized to $m(D)=1,{\mu}$ be an invariant measure on D defined by $d_{\mu}(z)=(1-{\mid}z{\mid}^2)^{-2}dm(z)$. For $f{\in}L^1(D^n,m{\times}{\cdots}{\times}m)$, Bf the Berezin transform of f is defined by, $$(Bf)(z_1,{\ldots},z_n)={\displaystyle\smashmargin{2}{\int\nolimits_D}{\cdots}{\int\nolimits_D}}f({\varphi}_{z_1}(x_1),{\ldots},{\varphi}_{z_n}(x_n))dm(x_1){\cdots}dm(x_n)$$. We prove that if $f{\in}L^1(D^2,{\mu}{\times}{\mu})$ is radial and satisfies ${\int}{\int_{D^2}}fd{\mu}{\times}d{\mu}=0$, then for every bounded radial function ${\ell}$ on $D^2$ we have $$\lim_{n{\rightarrow}{\infty}}{\displaystyle\smashmargin{2}{\int\int\nolimits_{D^2}}}(B^nf)(z,w){\ell}(z,w)d{\mu}(z)d{\mu}(w)=0$$. Then, using the above property we prove n-harmonicity of bounded function which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.268-271
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• 2003

There are several methods for the design of 2D filter. Notable among them is McClellan transform method. This transform allows us to obtain a high order 2D FIR filter through mapping the 1D frequency points of a 1D prototype FIR filter onto 2D frequency contours. We design 2D filter using this transform. Then we notice for mapping deviation of the 2D filter. In this paper, Quadratic programming (QP) method allows us to obtain coefficients of McClellan transform. Then we compare deviation of QP method with least-squares(LS) method. Elliptic filter is used for comparison. The optimal cutoff frequencies of a 1D filter are obtained directly from the QP method. Also several problem of LS method are solved.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.11a
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• pp.10-11
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• 2014

In a 2-dimensional (2D) Discrete Cosine Transform (DCT) hardware, a significant fraction of the total hardware area is contributed by the combinational logic used to perform 1-dimensional (2D) transform. The size of the non-combinational logic i.e. the transpose memory is dictated by the size of the largest transform supported. Hence, the optimization of hardware area is performed mainly for 1D-transform combinational logic. This paper demonstrates the use of Multiple Constant Multiplication (MCM) algorithm to reduce the combinational logic area. Partial optimizations are also described for the cases where the direct use of MCM algorithm doesn't meet the timing constraint. Experimental results show that 46% improvement in gate count is achieved for 32 point 1D DCT transform logic after using MCM optimization.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.2
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• pp.103-110
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• 1996

In this paper, we propose a unified systolic array for the computation of the 2D discrete cosine transform/discrete sine transform/discrete hartley transform (DCT/DST/DHT). The unified systeolic array for the 2D DCT/DST/DHT is a generalization of the unified systolic array for the 1D DCT/DST/DHT. In order to calculate the 2D transform, we compute 1D transforms along the row, transpose them, and obtain 1D transforms along the column. When we compare the proposed systolic array with the conventional method, our architecture exhibits a lot of advantages in terms of latency, throughput, and the number of PE's. The simulation results using very high speed integrated circuit hardware description language (VHDL), international standard language for hardware description, show the functional validity of the proposed architecture.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.6
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• pp.127-140
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• 2003

This paper develops a novel algorithm of computing 2 Dimensional Discrete Cosine Transform (2D-DCT) via Polynomial Transform (PT) converting 2D-DCT to the sum of 1D-DCTs. In computing N${\times}$M size 2D-DCT, the conventional row-column algorithm needs 3/2NMlog$_2$(NM)-2NM＋N＋M additions and 1/2NMlog$_2$(NM) additions and 1/2NMlog$_2$(NM) multiplications, while the proposed algorithm needs 3/2NMlog$_2$M＋NMlog$_2$N-M-N/2＋2 additions and 1/2NMlog$_2$M multiplications The previous polynomial transform needs complex operations because it applies the Euler equation to DCT. Since the suggested algorithm exploits the modular regularity embedded in DCT and directly decomposes 2D DCT into the sum of ID DCTs, the suggested algorithm does not require any complex operations.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• ETRI Journal
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• v.45 no.6
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• pp.1035-1045
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• 2023

We propose a novel graphics processing unit (GPU) algorithm that can handle a large-scale 3D fast Fourier transform (i.e., 3D-FFT) problem whose data size is larger than the GPU's memory. A 1D FFT-based 3D-FFT computational approach is used to solve the limited device memory issue. Moreover, to reduce the communication overhead between the CPU and GPU, we propose a 3D data-transposition method that converts the target 1D vector into a contiguous memory layout and improves data transfer efficiency. The transposed data are communicated between the host and device memories efficiently through the pinned buffer and multiple streams. We apply our method to various large-scale benchmarks and compare its performance with the state-of-the-art multicore CPU FFT library (i.e., fastest Fourier transform in the West [FFTW]) and a prior GPU-based 3D-FFT algorithm. Our method achieves a higher performance (up to 2.89 times) than FFTW; it yields more performance gaps as the data size increases. The performance of the prior GPU algorithm decreases considerably in massive-scale problems, whereas our method's performance is stable.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.86.4-86
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• 2002

1. Review of one dimensional M-transform 2. Definition of two dimensional(2D)M-transform 3. Properties of 2D M-transform 4. Mean, Autocorrelation 5. Crosscorrelation of input and output of a system 6. Application to fault detection of mechanical shape

• Journal of Korea Multimedia Society
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• v.21 no.1
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• pp.61-68
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• 2018

In this paper, we present an effective encryption algorithm for 3D printing models in the frequency domain of discrete cosine transform to prevent illegal copying, access in the secured storage and transmission. Facet data of 3D printing model is extracted to construct a three by three matrix that is then transformed to the frequency domain of discrete cosine transform. The proposed algorithm is based on encrypting the DC coefficients of matrixes of facets in the frequency domain of discrete cosine transform in order to generate the encrypted 3D printing model. Experimental results verified that the proposed algorithm is very effective for 3D printing models. The entire 3D printing model is altered after the encryption process. The proposed algorithm is provide a better method and more security than previous methods.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.