• The Journal of the Acoustical Society of Korea
• /
• v.21 no.3
• /
• pp.304-309
• /
• 2002

We propose the computation reduction method of real root method that is mainly used in the CELP (Code Excited Linear Prediction) vocoder. The real root method is that if polynomial equations have the real roots, we are able to find those and transform them into LSP. However, this method takes much time to compute, because the root searching is processed sequentially in frequency region. In this paper, to reduce the computation time of real root, we compare the real root method with two methods. In first method, we use the mal scale of searching frequency region that is linear below 1 kHz and logarithmic above. In second method, The searching frequency region and searching interval are ordered by each coefficient's distribution. In order to compare real root method with proposed methods, we measured the following two. First, we compared the position of transformed LSP (Line Spectrum Pairs) parameters in the proposed methods with these of real root method. Second, we measured how long computation time is reduced. The experimental results of both methods that the searching time was reduced by about 47% in average without the change of LSP parameters.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.21 no.6
• /
• pp.634-639
• /
• 2020

In general, the stability and response characteristics of the system can be improved by changing the pole position because a nonlinear system can be linearized by the product of a 1st and 2nd order system. Therefore, a controller that moves the pole can be designed in various ways. Among the other methods, LQ control ensures the stability of the system. On the other hand, it is difficult to specify the location of the pole arbitrarily because the desired response characteristic is obtained by selecting the weighting matrix by trial and error. This paper evaluated a method of selecting a weighting matrix of LQ control that moves multiple double poles with Jordan blocks to real poles. The relational equation between the double poles and weighting matrices were derived from the characteristic equation of the Hamiltonian system with a diagonal control weighting matrix and a state weighting matrix represented by two variables (ρ_d, ϕ_d). The Moving-Range was obtained under the condition that the state-weighting matrix becomes a positive semi-definite matrix. This paper proposes a method of selecting poles in this range and calculating the weighting matrices by the relational equation. Numerical examples are presented to show the usefulness of the proposed method.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.8 no.3
• /
• pp.563-568
• /
• 2007

We propose the computation reduction method of real root method that is used in the EVRC(Enhanced Variable Rate Codec) system. The real root method is that if polynomial equations have the real roots, we are able to find those and transform them into LSP. However, this method takes much time to compute, because the root searching is processed sequentially in frequency region. But, the important characteristic of LSP is that most of coefficients are occurred in specific frequency region. So, to reduce the computation time of real root, we used the met scale that is linear below 1kHz and logarithmic above. In order to compare real root method with proposed method, we measured the following two. First, we compared the position of transformed LSP(Line Spectrum Pairs) parameters in the proposed method with these of real root method. Second, we measured how long computation time is reduced. The experimental result is that the searching time was reduced by about 48% in average without the change of LSP parameters.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.2
• /
• pp.608-616
• /
• 2018

If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

• Proceedings of the KAIS Fall Conference
• /
• 2010.05a
• /
• pp.249-252
• /
• 2010

LPC 계수를 LSP 변환하는 방법에는 복소근, 실근, 비율 필터, 체비셰프 급수, 적응적 순차형 최소제곱 평균 방법(adaptive sequential LMS) 등이 있다. 이 방법들 중 음성 부호화기에서 주로 사용하는 실근 방법은 근을 구하기 위해 주파수 영역을 순차적으로 검색하기 때문에 계산시간이 많이 소요되는 단점을 갖는다. 본 논문에서는 LPC에서 LSP로 변환하는 4가지 고속 알고리즘을 제안한다. 첫 번째 방식에서는 검색간격에 멜 스케일을 적용하였고, 두 번째는 홀수번째 LSP 파라미터의 분포도를 이용하여 검색순서를 조정한 방법이다. 세 번째 방식과 네 번째 방식에서는 각각, 모음 특성, LSP 분포특성과 해상도를 이용하여 계산시간을 단축하였다. LSP 변환시간은 4가지 방법 모두 35~50% 단축되었다. 또한 실험결과에서는 각 알고리즘의 고유한 특성에 대하여 분석한다.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.21 no.1
• /
• pp.20-27
• /
• 2020

In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

• Korean Journal of Optics and Photonics
• /
• v.23 no.1
• /
• pp.17-22
• /
• 2012

An equivalent lens is a lens which has the same total power of refraction and the same paraxial imaging characteristics for the marginal rays as another lens, but has a different axial thickness. In this study, an analytic lens conversion from a thick lens to its equivalent lens is investigated, then it is shown that the equivalent lens is a solution of a quadratic equation. Every thick lens corresponds to one of two real roots of this quadratic equation. Therefore, except in the case of a unique solution, the equation has a conjugate solution, the other of the two roots. The conjugate solution has the same axial thickness, power, and paraxial imaging characteristics, but it has different shape and aberration characteristics. The characteristics of an equivalent lens and its conjugate solution are examined by using a sample lens.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.13 no.5
• /
• pp.85-91
• /
• 2013

For location based service and context awareness services, accurate indoor positioning technology is essential. The TDOA method that uses the range difference between signal source and receivers for estimating the location of the signal source, has estimation error due to measurement error. In this paper, a new algorithm is proposed to select the real root among calculated roots using the range difference information, and the estimated position of the signal source shows good accuracy compared to the existing method.