• Title/Summary/Keyword: difference sequence method

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Extraction of Initial Conditions For a Recursive Numerical Inverse z-Transform Method (차분방정식에 의한 역 z변환 계산을 위한 초기 조건의 추출)

  • Lee, Jae-Seok;Jeong, Tae-Sang
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.51 no.8
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    • pp.368-373
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    • 2002
  • The inverse z-transform of a z-domain expression of a sequence can be Performed in many different methods among which the recursive computational method is based on the difference equation. In applying this method, a few initial values of the sequence should be obtained separately. Although the existing method generates the right initial values of the sequence, its derivation and justification are not theoretically in view of the definition of z-transform and its shift theorems. In this paper a general approach for formulating a difference equation and for obtaining required initial values of a sequence is proposed, which completely complies to the definition of the z-transform and an interpretation of the validity of the existing method which is theoretically incorrect.

The connections and representation of Pascal Triangles, Difference sequences and Matrices (파스칼의 삼각형, 계차수열 및 행렬의 연계와 표현)

  • Kim Ik Pyo;Hwang Suk Geun
    • The Mathematical Education
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    • v.43 no.4
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    • pp.391-398
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    • 2004
  • It is well-known in the literature that the general term of a sequence can be represented by a linear combination of binomial coefficients. The theorem and its known proofs are not easy for highschool students to understand. In this paper we prove the theorem by a pictorial method and by a very short and easy inductive method to make the problem easy and accessible enough for highschool students.

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A NOTE ON DIFFERENCE SEQUENCES

  • Park, Jin-Woo
    • The Pure and Applied Mathematics
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    • v.16 no.3
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    • pp.255-258
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    • 2009
  • It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

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Discrete Optimization for Vibration Design of Composite Plates by Using Lamination Parameters

  • Honda, Shinya;Narita, Yoshihiro;Sasaki, Katsuhiko
    • Advanced Composite Materials
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    • v.18 no.4
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    • pp.297-314
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    • 2009
  • A design method is proposed to optimize the stacking sequence of laminated composite plates for desired vibration characteristics. The objective functions are the natural frequencies of the laminated plates, and three types of optimization problems are studied where the fundamental frequency and the difference of two adjacent frequencies are maximized, and the difference between the target and actual frequencies is minimized. The design variables are a set of discrete values of fiber orientation angles with prescribed increment in the layers of the plates. The four lamination parameters are used to describe the bending property of a symmetrically laminated plate, and are optimized by a gradient method in the first stage. A new technique is introduced in the second stage to convert from the optimum four lamination parameters into the stacking sequence that is composed of the optimum fiber orientation angles of all the layers. Plates are divided into sub-domains composed of the small number of layers and designed sequentially from outer domains. For each domain, the optimum angles are determined by minimizing the errors between the optimum lamination parameters obtained in the first step and the parameters for all possible discrete stacking sequence designs. It is shown in numerical examples that this design method can provide with accurate optimum solutions for the stacking sequence of vibrating composite plates with various boundary conditions.

A Visualization of the Solution of Truncated Series (절적(截積) 해법의 시각화)

  • Lee, Kyung Eon
    • Journal for History of Mathematics
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    • v.28 no.4
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    • pp.167-179
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    • 2015
  • We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

Temporal interpolator based on spatial filtering (공간 필터링에 근거한 시간축 내삽기)

  • 김종훈
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.33B no.8
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    • pp.60-67
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    • 1996
  • In this paper, we propose a new temporal interpolation method based on spatial filtering. Compared with the conventional method, the proposed one may use a few adjacent frames and apply temporal lowpass filtering. To develop this method, we follow the basic approach of sampling rate conversion. Additionally, we use some assumption of video sequence : moving object has constant velocity rigid translational motion. From them, spatial filtering for temporal sampling rate conversion is described. This method has a lot of noise immunity on a motion vector and doesn't make a great difference from the original frame. The interpolated frame shows moderate change even there is a great time difference. This method has exactly same description of motion adaptive spatial filter which has an efficient temporal band-limiting characteristics. It imposes the possibility to make video sequence with good pictural quality.

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Evaluation of sequence tracking methods for Compton cameras based on CdZnTe arrays

  • Lee, Jun;Kim, Younghak;Bolotnikov, Aleksey;Lee, Wonho
    • Nuclear Engineering and Technology
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    • v.53 no.12
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    • pp.4080-4092
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    • 2021
  • In this study, the performance of sequence tracking methods for multiple interaction events in specific CdZnTe Compton imagers was evaluated using Monte Carlo simulations. The Compton imager consisted of a 6 × 6 array of virtual Frisch-grid CZT crystals, where the dimensions of each crystal were 5 × 5 × 12 mm3. The sequence tracking methods for another Compton imager that consists of two identical CZT crystals arrays were also evaluated. When 662 keV radiation was incident on the detectors, the percentages of the correct sequences determined by the simple comparison and deterministic methods for two sequential interactions were identical (~80%), while those evaluated using the minimum squared difference method (55-59%) and Three Compton method (45-55%) for three sequential interactions, differed from each other. The reconstructed images of a 662 keV point source detected using single and double arrays were evaluated based on their angular resolution and signal-to-noise ratio, and the results showed that the double arrays outperformed single arrays.

Algorithm for Fault Location Estimation on Transmission Lines using Second-order Difference of a Positive Sequence Current Phasor

  • Yeo, Sang-Min;Jang, Won-Hyeok;Kim, Chul-Hwan
    • Journal of Electrical Engineering and Technology
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    • v.8 no.3
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    • pp.499-506
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    • 2013
  • The accurate estimation of a fault location is desired in distance protection schemes for transmission lines in order to selectively deactivate a faulted line. However, a typical method to estimate a fault location by calculating impedances with voltages and currents at relaying points may have errors due to various factors such as the mutual impedances of lines, fault impedances, or effects of parallel circuits. The proposed algorithm in this paper begins by extracting the fundamental phasor of the positive sequence currents from the three phase currents. The second-order difference of the phasor is then calculated based on the fundamental phasor of positive sequence currents. The traveling times of the waves generated by a fault are derived from the second-order difference of the phasor. Finally, the distance from the relaying point to the fault is estimated using the traveling times. To analyze the performance of the algorithm, a power system with EHV(Extra High Voltage) untransposed double-circuit transmission lines is modeled and simulated under various fault conditions, such as several fault types, fault locations, and fault inception angles. The results of the simulations show that the proposed algorithm has the capability to estimate the fault locations with high speed and accuracy.

Optimal test sequence generation scheme using non-minimal multiple UIO (비 최소 다중 UIO를 이용한 최적화된 시험열 생성)

  • 임상용;양대헌;강명호;송주석
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.22 no.10
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    • pp.2357-2363
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    • 1997
  • In this paepr, we show that the length of the test sequence can be reduced using non-minimal multiple UIO instead of minimal multiple UIO. Our test sequence generation method starts from the observation that Shen's approach cannot optimize the length of the test sequence whtn the difference between the number of incoming edge and that of outgoing edge is large. Usig the property, we propse a more efficient method to generate a UIO-based test sequence in terms of the length, and compares our method with other existing methods in terms of execution time for comformancetesting and time for generation of test sequence.

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A Blind Watermarking Technique Using Difference of Approximation Coefficients in Wavelet Domain (웨이블릿 영역에서 근사 계수의 증감 정보를 이용한 블라인드 워터마크)

  • 윤혜진;성영경;최태선
    • Proceedings of the IEEK Conference
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    • 2002.06d
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    • pp.219-222
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    • 2002
  • In this paper, we propose a new blind image watermarking method in wavelet domain. It is necessary to find out watermark insertion location in blind watermark. We use horizontal and vertical difference of LL components to select watermark insertion location, because increment or decrement of successive components is rarely changed in LL band. A pseudo-random sequence is used as a watermark. Experimental results show that the proposed method is robust to various kinds of attacks such as JPEG lossy compression, averaging, median filtering, resizing, histogram equalization, and additive Gaussian noise.

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