• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.93-101
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• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5A
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• pp.333-340
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• 2003

In this paper, we propose a new turbo-coded orthogonal frequency division multiplexing (OFDM) transmission scheme that can improve greatly the performance by making all the turbo-coded symbols have the same reliability for OFDM transmission over a frequency selective fading channel. The same reliability, that is, the same fading can be accomplished through multiplexing of turbo-coded symbols using distinct orthogonal codes and spreading over the whole effective subcarriers (hereafter, called as the orthogonal code multiplexing (OCM)). As for the orthogonal code selection, we choose the set of the discrete Fourier transform (DFT) basis sequences, since the code set holds the orthogonality irrespective of the length and also has the equal energy property. We perform computer simulations using the Log-maximum-a-posteriori (Log-MAP) algorithm for iterative decoding in order to assess the performance of the proposed transmission scheme.

• Wind and Structures
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• v.3 no.4
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• pp.221-241
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• 2000

Structural dynamics usually applies modal transformation rules aimed at de-coupling and/or minimizing the equations of motion. Proper orthogonal decomposition provides mathematical and conceptual tools to define suitable transformed spaces where a multi-variate and/or multi-dimensional random process is represented as a linear combination of one-variate and one-dimensional uncorrelated processes. Double modal transformation is the joint application of modal analysis and proper orthogonal decomposition applied to the loading process. By adopting this method the structural response is expressed as a double series expansion in which structural and loading mode contributions are superimposed. The simultaneous use of the structural modal truncation, the loading modal truncation and the cross-modal orthogonality property leads to efficient solutions that take into account only a few structural and loading modes. In addition the physical mechanisms of the dynamic response are clarified and interpreted.

• Wind and Structures
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• v.10 no.2
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• pp.153-176
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• 2007

The Proper Orthogonal Decomposition (POD) is a statistical method particularly suitable and versatile for dealing with many problems concerning wind engineering and several other scientific and humanist fields. POD represents a random process as a linear combination of deterministic functions, the POD modes, modulated by uncorrelated random coefficients, the principal components. It owes its popularity to the property that only few terms of the series are usually needed to capture the most energetic coherent structures of the process, and a link often exists between each dominant mode and the main mechanisms of the phenomenon. For this reason, POD modes are normally used to identify low-dimensional subspaces appropriate for the construction of reduced models. This paper provides a state-of-the-art and some prospects on POD, with special regard to its framework and applications in wind engineering. A wide bibliography is also reported.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1027-1040
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• 2012

The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.

• Journal of the Optical Society of Korea
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• v.20 no.4
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• pp.476-480
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• 2016

For the application of multiusers, the arrangement and distribution of the keys is a much concerning problem in a cryptosystem. In this paper, we propose an optical encryption scheme with multiple users based on computational ghost imaging (CGI) and orthogonal modulation. The CGI encrypts the secret image into an intensity vector rather than a complex-valued matrix. This will bring convenience for post-processing and transmission of the ciphertext. The orthogonal vectors are taken as the address codes to distinguish users and avoid cross-talk. Only the decryption key and the address code owned by an authorized user are matched, the secret image belonging to him/her could be extracted from the ciphertext. Therefore, there are two security levels in the encryption scheme. The feasibility and property are verified by numerical simulations.

• Journal of Korean Society for Quality Management
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• v.45 no.4
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• pp.889-902
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• 2017

Purpose: The orthogonality and trace optimal properties are desirable for constructing designs of experiments. This article focuses on the determination of the sizes of experiments for the balanced trace optimal resolution-V fractional factorial designs for 2-level factorial designs, which have near-orthogonal properties. Methods: In this paper, first we introduce the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$, by exploiting the partially balanced array for various cases of experimental sizes. Moreover some orthogonality criteria are also suggested with which the degree of the orthogonality of the designs can be evaluated. And we appraise the orthogonal properties of the introduced designs from various aspects. Results: We evaluate the orthogonal properties for the various experimental sizes of the balanced trace optimal resolution-V fractional factorial designs of the 2-level factorials in which each factor has two levels. And the near-orthogonal 2-level balanced trace optimal resolution-V fractional factorial designs are suggested, which have adequate sizes of experiments. Conclusion: We can construct the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$ by exploiting the results suggested in this paper, which have near-orthogonal property and appropriate experimental sizes. The suggested designs can be employed usefully especially when we intend to analyze both the main effects and two factor interactions of the 2-level factorial experiments.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.497-502
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• 2006

An asymmetric Fuglede-Putnam theorem for $p$-hyponormal operators and class ($\mathcal{Y}$) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2004.11a
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• pp.108-108
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• 2004

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.3C
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• pp.331-337
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• 2007

In this paper, we propose a novel Walsh coded training signal design and Walsh decoding method to estimate the channel response in MIMO-OFDM systems. The Walsh coded training signals are designed to have orthogonal property in time domain. Using the orthogonal property, the Walsh decoding process makes it possible to separate the desired training signal from the received signal and to estimate the channel response. The computer simulation results show that the proposed method exhibits almost the same performance as Li's original method using the optimal training sequence, even though the proposed method has much lower complexity.