• Title/Summary/Keyword: Square root

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A Square Root Normalized LMS Algorithm for Adaptive Identification with Non-Stationary Inputs

  • Alouane Monia Turki-Hadj
    • Journal of Communications and Networks
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    • v.9 no.1
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    • pp.18-27
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    • 2007
  • The conventional normalized least mean square (NLMS) algorithm is the most widely used for adaptive identification within a non-stationary input context. The convergence of the NLMS algorithm is independent of environmental changes. However, its steady state performance is impaired during input sequences with low dynamics. In this paper, we propose a new NLMS algorithm which is, in the steady state, insensitive to the time variations of the input dynamics. The square soot (SR)-NLMS algorithm is based on a normalization of the LMS adaptive filter input by the Euclidean norm of the tap-input. The tap-input power of the SR-NLMS adaptive filter is then equal to one even during sequences with low dynamics. Therefore, the amplification of the observation noise power by the tap-input power is cancelled in the misadjustment time evolution. The harmful effect of the low dynamics input sequences, on the steady state performance of the LMS adaptive filter are then reduced. In addition, the square root normalized input is more stationary than the base input. Therefore, the robustness of LMS adaptive filter with respect to the input non stationarity is enhanced. A performance analysis of the first- and the second-order statistic behavior of the proposed SR-NLMS adaptive filter is carried out. In particular, an analytical expression of the step size ensuring stability and mean convergence is derived. In addition, the results of an experimental study demonstrating the good performance of the SR-NLMS algorithm are given. A comparison of these results with those obtained from a standard NLMS algorithm, is performed. It is shown that, within a non-stationary input context, the SR-NLMS algorithm exhibits better performance than the NLMS algorithm.

A Study on a Morphological Identification of Notoginseng Radix (삼칠근(三七根)의 형태(形態)에 관한 연구(硏究))

  • Moon, Seong-Ho;Lee, Young-Jong
    • The Korea Journal of Herbology
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    • v.23 no.2
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    • pp.25-31
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    • 2008
  • Objectives : In order to distinguish morphological characteristics of trunk bark and root bark of Ulmus davidiana var. japonica (Rehder) Nakai and the trunk bark and root bark of Hemiptelea davidii Planchon were sampled and compared in terms of their external and internal features with flour states according to their medical use, through microscopic examination. Methods : The slice of the tested material made by paraffin section technique was colored with Safranine Malachite Green contrast methods, and the flour of it was mounted by the liquid made by the same ratio of each of glycerin, acetic acid, and water, and then observed and photographed by olymphus-BHT. Results : 1. Internal Features 1) A large parenchymatous cell was observed in the phloem of the slice of both trunk bark and root bark of Ulmi Cortex, However, both of the trunk bark and root bark of Hemipteleae Cortex did not have parenchymatous cell in the phloem; instead, stone cells including much square crystal of calcium oxalate were distributed around fiber bundle, and the parenchymatous cell included much druse crystal of calcium oxalate. 2) In both the Ulmi Cortex and Hemipteleae Cortex, rhytidome was observed in trunk bark, but not in root bark, but in the parenchymatous cell of the root bark of the Ulmi Cortex contained starch grain. 2. Flour States 1) In the flour of root bark of the Ulmi Cortex, a large parenchymatous cell was observed. However, in the flour of trunk bark and root bark of Hemipteleae Cortex, no parenchymatous eel was found; instead, stone cell including square crystal of calcium oxalate and druse crystal of calcium oxalate were observed. 2) There was no remarkable difference between the trunk bark and root bark of Hemipteleae Cortex. However, starch grain was contained in the parenchymatous cell of the root bark of Ulmi Cortex but not in the trunk bark of it. Conclusions : There were some morphological differences in external, internal, and flour parts of Ulmi Cortex and Hemipteleae Cortex. In particular, there was a morphological difference in flour states between the trunk bark and root bark of Ulmi Cortex, it is possible to use microscope to distinguish their flour states.

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Morphologic Changes of L5 Root at Coronal Source Images of MR Myelography in Cases of Foraminal or Extraforaminal Compression

  • Kim, Soo-Beom;Jang, Jee-Soo;Lee, Sang-Ho
    • Journal of Korean Neurosurgical Society
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    • v.46 no.1
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    • pp.11-15
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    • 2009
  • Objective: Two findings easily found at coronal source images of MR myelography (MRM) were evaluated : dorsal root ganglion (DRG) swelling and running course abnormality (RCA) of L5 exiting root at foramen or extraforamen. We tried to find the sensitivity of each finding when root was compressed. Methods: From 2004 July to 2006, one hundred and ten patients underwent one side paraspinal decompression for their L5 root foraminal or extraforaminal compression at L5-S1 level. All kinds of conservative treatments failed to improve leg symptom for several months. Before surgery, MRI, CT and MRM were done. Retrospective radiologic analysis for their preoperative MRM coronal source images was done to specify root compression sites and L5 root morphologic changes. Results: DRG swelling was found in 66 (60%) of 110 patients. DRG swelling has statistically valuable meaning in foraminal root compression (chi-square test, p<0.0001). Seventy-two (66%) in 110 patients showed abnormal alteration of running course. Abnormal running course has statistically valuable meaning in foraminal or extraforaminal root compression (chi-square test, p<0.0001). Conclusion: Three-dimensional MRM provides precise thin sliced coronal images which are most close to real operative views. DRG swelling and running course abnormality of L5 exiting root are two useful findings in diagnosing L5 root compression at L5-S1 foramen or extraforamen. MRM is thought to provide additional diagnostic accuracy expecially in L5-S1 foraminal and extraforaminal area.

Damage detection of subway tunnel lining through statistical pattern recognition

  • Yu, Hong;Zhu, Hong P.;Weng, Shun;Gao, Fei;Luo, Hui;Ai, De M.
    • Structural Monitoring and Maintenance
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    • v.5 no.2
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    • pp.231-242
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    • 2018
  • Subway tunnel structure has been rapidly developed in many cities for its strong transport capacity. The model-based damage detection of subway tunnel structure is usually difficult due to the complex modeling of soil-structure interaction, the indetermination of boundary and so on. This paper proposes a new data-based method for the damage detection of subway tunnel structure. The root mean square acceleration and cross correlation function are used to derive a statistical pattern recognition algorithm for damage detection. A damage sensitive feature is proposed based on the root mean square deviations of the cross correlation functions. X-bar control charts are utilized to monitor the variation of the damage sensitive features before and after damage. The proposed algorithm is validated by the experiment of a full-scale two-rings subway tunnel lining, and damages are simulated by loosening the connection bolts of the rings. The results verify that root mean square deviation is sensitive to bolt loosening in the tunnel lining and X-bar control charts are feasible to be used in damage detection. The proposed data-based damage detection method is applicable to the online structural health monitoring system of subway tunnel lining.

The Effect of the Physical Therapy Treatment Room Environment Using Microwave Diathermy on the Autonomic Nervous System of Human Body (극초단파치료기를 사용하는 물리치료실의 환경이 물리치료사의 인체자율신경계에 미치는 영향)

  • Shin, Han-Ki;Lee, Tae-Kyu;Jun, Je-Yoon;Kim, Ju-Seung;Kang, Jong-Ho
    • Journal of the Korean Society of Physical Medicine
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    • v.10 no.1
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    • pp.37-43
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    • 2015
  • PURPOSE: The purpose of this study is to investigate the effect of the physical therapy treatment room environment using microwave diathermy on the autonomic nervous system of human body. METHODS: Participants were 24 healthy adults. Standard deviation of all normal R-R intervals(SDNN), root mean square of successive differences(RMSSD), low frequency(LF), high frequency(HF), LF/HF ratio were compared in microwave irradiation and non-irradiation group. Data were analyzed in Wilcoxon's signed-ranks test and Mann-Whitney U test. RESULTS: Standard deviation of all normal R-R intervals (SDNN), root mean square of successive differences (RMSSD), low frequency(LF), high frequency(HF), LF/HF ratio were not significantly different in microwave irradiation group. Standard deviation of all normal R-R intervals(SDNN), root mean square of successive differences (RMSSD), low frequency(LF), high frequency(HF), LF/HF ratio were not significantly different in microwave non-irradiation group. Standard deviation of all normal R-R intervals(SDNN), root mean square of successive differences (RMSSD), low frequency(LF), high frequency(HF), LF/HF ratio were not significantly different between two groups. CONCLUSION: There was no significant change in the sympathetic nervous system and parasympathetic nervous system regardless of the presence of microwave irradiation. There was no significant change in the autonomic nervous system adaptability regardless of the presence of microwave irradiation.According to this study, microwave diathermy does not have significant effect on the autonomic nervous system.Future study is necessary to investigate the long term effect of the physical therapy treatment room environment using microwave diathermy on the autonomic nervous system of the human body.

Suggestion for a splitting technique of the square-root operator of three dimensional acoustic parabolic equation based on two variable rational approximant with a factored denominator (인수분해 된 분모를 갖는 두 변수 유리함수 근사에 기반한 3차원 음향 포물선 방정식 제곱근 연산자의 분할기법 제안)

  • Lee, Keunhwa
    • The Journal of the Acoustical Society of Korea
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    • v.36 no.1
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    • pp.1-11
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    • 2017
  • In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

A Variable Latency Goldschmidt's Floating Point Number Square Root Computation (가변 시간 골드스미트 부동소수점 제곱근 계산기)

  • Kim, Sung-Gi;Song, Hong-Bok;Cho, Gyeong-Yeon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.9 no.1
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    • pp.188-198
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    • 2005
  • The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

A Study of Threshold Determination of The GPS measurement failure using GPS Code-Carrier Divergence Test (GPS 의사거리-반송파 위상 측정치의 고장검출을 위한 임계값 결정 연구)

  • Son, Eunseong;Kim, Koon-Tack;Im, Sung-Hyuck;Lee, Eun-Sung;Heo, Moon Beom;Nam, Gi-Wook
    • Journal of the Korean Society for Aviation and Aeronautics
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    • v.24 no.1
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    • pp.10-15
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    • 2016
  • In this study, The code-carrier divergence test was applied to GPS measurements, and the results were compared and analyzed. The GPS data used for the threshold determination were obtained from Global Navigation Satellite System permanent stations built by the Korea Aerospace Research Institute. At each permanent station, identical dual-frequency receiver and choke ring antenna with radome are installed. The analysis method, root mean square values were compared and analyzed for each permanent station and satellite. As a result, the root mean square value generally decreased as the satellite elevation angle increased although the trend was gentle. Threshold were finally selected based on the average and standard deviation of root mean square for each permanent station. For improving of availability and continuity in real-time operation when the threshold is over the limits, Code-Carrier divergence test values are initialized.

Initial Point Optimization for Square Root Approximation based on Newton-Raphson Method (Newton-Raphson 방식의 제곱근 근사를 위한 초기값의 최적화)

  • Choi Chang-Soon;Lee Jin-Yong;Kim Young-Lok
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.43 no.3 s.345
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    • pp.15-20
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    • 2006
  • A Newton-Raphson Method for table driven algorithm is presented in this paper. We concentrate the approximation of square root by using Newton-Raphson method. We confirm that this method has advantages of accurate and fast processing with optimized initial point. Hence the selection of the fitted initial points used in approximation of Newton-Raphson algorithm is important issue. This paper proposes that log scale based on geometric wean is most profitable initial point. It shows that the proposed method givemore accurate results with faster processing speed.

Prediction of the interest spread using VAR model (벡터자기회귀모형에 의한 금리스프레드의 예측)

  • Kim, Junhong;Jin, Dalae;Lee, Jisun;Kim, Suji;Son, Young Sook
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.6
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    • pp.1093-1102
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    • 2012
  • In this paper, we predicted the interest spread using the VAR (vector autoregressive) model. Variables used in the VAR model were selected among 56 domestic and foreign macroeconomic time series through crosscorrelation and Granger causality test. The performance of the VAR model was compared with the univariate time series model, AR (autoregressive) model, in view of MAPE (mean absolute percentage error) and RMSE (root mean square error) of forecasts for the last twelve months.