• Journal of IKEEE
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• v.19 no.3
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• pp.378-384
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• 2015

In conventional HEVC inverse core transform architectures, extra $n{\times}n$ inverse transform block is added to $2n{\times}2n$ inverse transform block, and it operates as one $2n{\times}2n$ inverse transform block or two $n{\times}n$ inverse transform blocks. Thus, same number of pixels are processed in the same time, but it suffers from increased hardware size due to extra $n{\times}n$ inverse transform block. To avoid this problem, a novel $8{\times}8$ HEVC inverse core transform architecture was proposed to eliminate extra $4{\times}4$ inverse transform block based on multiplier reuse. This paper extends this approach and proposes a novel HEVC $16{\times}16$ inverse core transform architecture. Its frame processing time is same in $4{\times}4$, $8{\times}8$, and $16{\times}16$ inverse core transforms, and reduces gate counts by 13%.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1773-1781
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• 2018

The Radon transform introduced by J. Radon in 1917 is the integral transform which is widely applicable to tomography. Here we study the discrete version of the Radon transform. More precisely, when $C({\mathbb{Z}}^n_p)$ is the set of complex-valued functions on ${\mathbb{Z}}^n_p$. We completely determine the subset of $C({\mathbb{Z}}^n_p)$ whose elements can be recovered from its Radon transform on ${\mathbb{Z}}^n_p$.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1065-1082
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• 2012

In this paper we first investigate the existence of the generalized Fourier-Feynman transform of the functional F given by $$F(x)={\hat{\nu}}((e_1,x)^{\sim},{\ldots},(e_n,x)^{\sim})$$, where $(e,x)^{\sim}$ denotes the Paley-Wiener-Zygmund stochastic integral with $x$ in a very general function space $C_{a,b}[0,T]$ and $\hat{\nu}$ is the Fourier transform of complex measure ${\nu}$ on $B({\mathbb{R}}^n)$ with finite total variation. We then define two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.4B
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• pp.418-422
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• 2001

4-점 리버스 자켓 변환 (4-Point Reverse Jacket transform)의 장점 중의 하나는 4-점 fast Fourier transform(FFT)시 야기되는 실수 또는 복소수 곱셈을 행렬분해(matrix decomposition)를 이용, 곱셈인자를 모두 대각행렬에만 집중시킨, 매우 간결하고 효율적인 알고리즘이라는 점이다. 본 논문에서는 이를 N 점 FFT에 적용하는 알고리즘을 제안한다. 이 방법은 기존의 다른 변환형태보다 확장하거나 구조를 파악하기에 매우 용이하다.

• The Journal of the Acoustical Society of Korea
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• v.26 no.5
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• pp.214-219
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• 2007

This paper proposes a new IFFT(Inverse Fast Fourier Transform) algorithm, which is proper for IMDCT(Inverse Modified Discrete Cosine Transform) of MPEG-2 AAC(Advanced Audio Coding) decoder. The $2^n$(N-point) type IMDCT is the most powerful among many IMDCT algorithms, however it includes IFFT that requires many calculation cycles. The IFFT used in $2^n$(N-point) type IMDCT employ the bit-reverse data arrangement of inputs and N/4-point complex IFFT to reduce the calculation cycles. We devised a new data arrangement method of IFFT input and $N/4^{n+1}$-type IFFT and thus we can reduce multiplication cycles, addition cycles, and ROM size.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.6
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• pp.272-282
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• 2001

This paper developed improved fast Walsh transform based on dyadic-ordered fast Walsh transform, then regenerated signal flow graph of improved fast Walsh transform, and used it for digital filtering, and then measured fundamental frequency and harmonics for current and voltage signals of power system. Using the improved fast Walsh transform, we present a new algorithm which reduces the computational amount, and it can consequently calculate the real and imaginary components for current and voltage signals of power system in sampling intervals. The calculation amount is reduced to 2(N-1) at N samples to measure full harmonics using developed algorithm. When, in single harmonic measuring, it needs only 2(log2N-1) additions and subtractions.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.515-521
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• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.517-526
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• 2001

In this paper, we study the continuous wavelet transform on the Heisenberg group H$^n$, and describe the related continuous multiscale analysis. By using the wavelet packet transform we obtain a reconstruction formula on L$^2$(H$^n$).