• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.93-111
• /
• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Korean Journal of Mathematics
• /
• v.9 no.2
• /
• pp.133-147
• /
• 2001

In this paper, we introduce the concepts of multiple $L_p$ analytic Fourier-Feynman transform ($1{\leq}p$ < ${\infty})$ and a convolution product of functionals on abstract Wiener space and verify the existence of the multiple $L_p$ analytic Fourier-Feynman transform for functionls in the Fresnel class. Moreover, we verify that the Fresnel class is closed under the $L_p$ analytic Fourier-Feynman transformation and the convolution product, respectively. And we establish some relationships among the multiple $L_p$ analytic Fourier-Feynman transform and the convolution product on the Fresnel class.

• Proceedings of the IEEK Conference
• /
• 2002.06d
• /
• pp.41-44
• /
• 2002

In the communications systems with diversity, we are commonly faced on needing of new source coding technique, error resilient coding. The error resilient coding addresses the coding algorithm that has the robustness to unreliability of communications channel. In recent years, many error resilient coding techniques were proposed such as data partitioning, resynchronization, error detection, concealment, reference picture selection and multiple description coding (MDC). In this paper, we proposed an MDC using whitening transform. The conventional MDC using correlating transform is need additional information to decode the image. But, if an image is transformed using the whitening transform, the additional information is not necessary to transform because the coefficients of whitening transform have uni-variance statistics.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.1
• /
• pp.79-99
• /
• 2006

In this paper, we define a class of functional defined on a very general function space $C_{a,b}[0,T]$ like a Fresnel class of an abstract Wiener space. We then define the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product of functionals on function space $C_{a,b}[0,T]$. Finally, we establish some relationships between the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\mathcal{F}(C_{a,b}[0,T])$.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.55 no.5
• /
• pp.205-215
• /
• 2006

In this paper an optical power meter using Hadamard transform, which can be used in multiple channel optical elements alignment system, is proposed. A traditional optical power meter in multiple channel optical elements alignment system is able to judge how well the elements are aligned each other by measuring optical power of the first and the last two channels with at least two detectors. It has critical drawback that the alignment accuracy per channel is dependent on the number of detectors. The proposed optical power meter can get noise reduction by the Hadamard transform based multiplexing technique. The Hadamard transform based multiplexing technique using spatial light modulators is distinguished by the best enhancement of signal-to-noise ratio (SNR) for the reconstructed signals. Moreover, the noise reduction increases with increasing the order of multiplexing, namely the number of optical element channels. The proposed system is implemented by PDLC (Polymer Dispersed Liquid Crystal) mask which is operated by electric filed and generates optimal multiplexing patterns based on the Hadamard transform and single detector. It means that we obtain not only the each channel's optical power of multiple channel elements at once but also the best enhancement of SNR with single detector. Experimental results show that the proposed optical power meter is suitable for an active optical alignment system for multiple channel optical elements.

• Current Optics and Photonics
• /
• v.2 no.4
• /
• pp.315-323
• /
• 2018

A new multiple-image encryption scheme that is based on a compressive ghost imaging concept along with a Fourier transform sampling principle has been proposed. This further improves the security of the scheme. The scheme adopts a Fourier transform to sample the original multiple-image information respectively, utilizing the centrosymmetric conjugation property of the spatial spectrum of the images to obtain each Fourier coefficient in the most abundant spatial frequency band. Based on this sampling principle, the multiple images to be encrypted are grouped into a combined image, and then the compressive ghost imaging algorithm is used to improve the security, which reduces the amount of information transmission and improves the information transmission rate. Due to the presence of the compressive sensing algorithm, the scheme improves the accuracy of image reconstruction.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.397-413
• /
• 2009

In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.

• East Asian mathematical journal
• /
• v.31 no.1
• /
• pp.135-144
• /
• 2015

In this paper we establish several formulas for multiple integral transform of functionals defined on abstract Wiener space. We then use the these results to establish several basic formulas involving multiple convolution products.

• Kyungpook Mathematical Journal
• /
• v.20 no.1
• /
• pp.121-127
• /
• 1980

In the present paper the multiple generalized prolate spheroidal wave transform has been developed and its useful operational property has been discussed. As an application of this new transform we have considered the non-homogeneous cubical region. The source of heat generation lies inside it and is dependent upon temperature, and the conductivity is variable.

• JSTS:Journal of Semiconductor Technology and Science
• /
• v.7 no.4
• /
• pp.247-253
• /
• 2007

In this paper, a high throughput multiple transform architecture for H.264 Fidelity Range Extensions (FRExt) is proposed. New techniques are adopted which (1) regularize the $8{\times}8$ integer forward and inverse DCT transform matrices, (2) divide them into four $4{\times}4$ sub-matrices so that simple fast butterfly algorithm can be used, (3) because of the similarity of the sub-matrices, mixed butterflies are proposed that all the sub-matrices of $8{\times}8$ and matrices of $4{\times}4$ forward DCT (FDCT), inverse DCT (IDCT) and Hadamard transform can be merged together. Based on these techniques, a hardware architecture is realized which can achieve throughput of 1.488Gpixel/s when processing either $4{\times}4\;or\;8{\times}8$ transform. With such high throughput, the design can satisfy the critical requirement of the real-time multi-transform processing of High Definition (HD) applications such as High Definition DVD (HD-DVD) ($1920{\times}1080@60Hz$) in H.264/AVC FRExt. This work has been synthesized using Rohm 0.18um library. The design can work on a frequency of 93MHz and throughput of 1.488Gpixel/s with a cost of 56440 gates.