• Journal of the Korean Mathematical Society
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• v.33 no.3
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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.

• The Pure and Applied Mathematics
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• v.16 no.4
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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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• v.31 no.4
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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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• v.1 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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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).

• Journal of the Korea Computer Industry Society
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• v.8 no.3
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• pp.155-166
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• 2007

In this paper, captured face-image was pre-processing, segmentation, and extracting features from thinning by differential operator and minute-delineation. A straight line in slope-intercept form was transformed at the $r-\theta$ domain using Hough Transform, instead of Housdorff distance are extract feature as length, rotation, displacement of lines from thinning line components by differentiation. This research proposed a new approach compare with Hough Transformation and Housdorff Distance for face recognition so that Hough transform is simple and fast processing of face recognition than processing by Housdorff Distance. Rcognition accuracy rate is that Housdorff method is higher than Hough transformation's method.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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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.

• Proceedings of the KIEE Conference
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• 1988.07a
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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.

• Proceedings of the KSRS Conference
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• 2003.11a
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.1
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• pp.119-126
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• 2012

H.264/AVC can use three transforms depending on types of residual data which are to be coded. H.264/AVC always executes $4{\times}4$ DCT transform. In $16{\times}16$ intra mode only, $4{\times}4$ Hadamard transform for luma DC coefficients and $2{\times}2$ Hadamard transform for chroma DC coefficients are performed additionally. Quantization is carried out to achieve further data compression after transform coding is completed. In this paper, the hardware implementation for DCT transform, Hadamard transform and quantization is studied. Especially, the proposed architecture adopting the pipeline technique can output a quantized result per clock cycle after 33-clock cycle latency. The proposed architecture is coded in Verilog-HDL and synthesized using Xilinx 7.1i ISE tool. The operating frequency is 106MHz at SPARTAN3S-1000. The designed IP can process maximum 33-frame at $1920{\times}1080$ HD resolution.