• 대한수학회지
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• 제33권3호
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• Smart Structures and Systems
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• 제1권2호
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• pp.185-215
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• 2005

Advanced signal processing techniques have been long introduced and widely used in structural health monitoring (SHM) and nondestructive evaluation (NDE). In our research, we applied several signal processing approaches for our embedded ultrasonic structural radar (EUSR) system to obtain improved damage detection results. The EUSR algorithm was developed to detect defects within a large area of a thin-plate specimen using a piezoelectric wafer active sensor (PWAS) array. In the EUSR, the discrete wavelet transform (DWT) was first applied for signal de-noising. Secondly, after constructing the EUSR data, the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used for the time-frequency analysis. Then the results were compared thereafter. We eventually chose continuous wavelet transform to filter out from the original signal the component with the excitation signal's frequency. Third, cross correlation method and Hilbert transform were applied to A-scan signals to extract the time of flight (TOF) of the wave packets from the crack. Finally, the Hilbert transform was again applied to the EUSR data to extract the envelopes for final inspection result visualization. The EUSR system was implemented in LabVIEW. Several laboratory experiments have been conducted and have verified that, with the advanced signal processing approaches, the EUSR has enhanced damage detection ability.

• 충청수학회지
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• 제23권2호
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• pp.349-362
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• 2010

We establish the various relationships among the integral transform ${\mathcal{F}}_{{\alpha},{\beta}}F$, the convolution product $(F*G)_{\alpha}$ and the first variation ${\delta}F$ for a class of functionals defined on K(Q), the space of complex-valued continuous functions on $Q=[0,S]{\times}[0,T]$ which satisfy x(s, 0) = x(0, t) = 0 for all $(s,t){\in}Q$. And also we obtain Parseval's and Plancherel's relations for the integral transform of some functionals defined on K(Q).

• 한국컴퓨터산업학회논문지
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• 제8권3호
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• pp.155-166
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• 2007

본 연구에서는 얼굴 영상을 캡쳐하여 전 처리한 후 얼굴영역을 분리하고, 분리된 얼굴 영역에서 미분 연산자와 최소 형태를 세선화하여 특징을 추출하였다. Hough Transform은 $r-\theta$ 평면에서 직선의 기울기와 절편으로 변환되며, 반면 Housdorff distance는 세선화된 영상에서 선분을 추출하여 길이, 회전, 천이 특징을 추출하였다. 사람마다 다른 특징들을 추출하여 Housdorff distance과 Hough Transform에 관하여 비교분석 결과 Hough변환의 복잡도가 더 적은 것으로 판단되었다. 인식율은 Housdorff Distance를 이용한 인식율이 Hough Transformation에 비해 조금 높게 나타났다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2006-2009
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• 2005

This paper presents a method for registering images using phase correlation technique in fourier domain, hough transform and multi-resolution wavelet. To register images, source and input images are transformed to wavelet domain. An angular transition can be obtained by applying hough transform technique followed by phase correlation. Then we apply phase correlation technique to find x-axis and y-axis transition. We apply wavelet transform to reduce processing time and also use its coefficients as edge information instead of canny detector. With multi-resolution property of wavelet transform, registration time can be greatly reduced. After we get all transition parameters, we transform the input images according to these parameters. Then, we compose and blend all images into a new large image with details of all source images. From our experiment, we can find the accurate transition both x-y translation and angular transition with less error.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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• pp.14-16
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• 1988

With the development of VLSI technology, research on special processors for high-speed processing is on the increase and studies are focused on designing VLSI-oriented processors for signal processing. This paper processes a one-dimensional systolic array for Discrete Hartley Transform implementation and also processes processing element which is well described for algorithm. The discrete Hartley Transform(DHT) is a real-valued transform closely related to the DFT of a real-valued sequence can be exploited to reduce both the storage and the computation requried to produce the transform of real-valued sequence to a real-valued spectrum while preserving some of the useful properties of the DFT is something preferred. Finally, the architecture of one-dimensional 8-point systolic array, the detailed diagram of PE, total time units concept on implementation this arrays, and modularity are described.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2003년도 Proceedings of ACRS 2003 ISRS
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• pp.192-194
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• 2003

Since the details in quasi-homogeneous region will be destroyed from the conventional global image enhancement method such as histogram equalization. This defect is caused by the saturation of gray level in equalization process. So the local histogram equalization for each quasi-homogeneous region will be used in order to improve the details in the region itself. To obtain the quasi- homogeneous regions, the original image must be segmented. Here we applied the watershed transform to the interesting image. Since the watershed transform is based on mathematical morphology, therefore, the regions touch can be effectively separated. Hence two adjacent regions which have the similar gray pixels will be split off. The process will be independently applied to three different spectral images. Then three different colors are assigned to each processed image in order to produce a color composite image. By the proposed algorithm, the result image shows the better perception on image details. Therefore, the high efficiency of image classification can be obtained by using this color image.

• 한국정보통신학회논문지
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• 제16권1호
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• pp.119-126
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• 2012

H.264/AVC는 부호화되는 잉여 데이터의 유형에 따라 3개의 변환을 사용할 수 있다. $4{\times}4$ DCT 변환은 항상 수행되며, $16{\times}16$ 인트라 모드인 경우에는 추가적으로 휘도 DC 계수에는 $4{\times}4$ 하다마드 변환을 수행하고, 색체 DC 계수에는 $2{\times}2$ 하다마드 변환을 수행한다. 변환 코딩을 완료한 이후에 한층 더한 데이터 압축을 위해 양자화가 수행된다. 본 논문에서는 H.264/AVC에 중요한 역할을 하는 DCT 변환, 하다마드 변환 및 양자화에 대한 하드웨어적인 구현에 대해 연구하였다. 특히 파이프라인 기법을 적용하여 33클럭의 대기지연시간 이후에는 매 클럭 당 1개의 양자화된 결과를 출력할 수 있는 아키텍쳐를 제안하였다. 제안한 아키텍쳐는 Verilog HDL로 코딩되고, Xilinx 7.1i ISE툴을 사용하여 합성하고 검증하였다. 합성 결과 SPARTAN3S-1000 디바이스에서 동작 주파수는 106MHz이다. $1920{\times}1080$ HD 영상 프레임의 경우 최대 33프레임을 처리할 수 있다.