• Journal of Computational Design and Engineering
• /
• v.1 no.2
• /
• pp.116-127
• /
• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Journal of the Korean Statistical Society
• /
• v.22 no.2
• /
• pp.249-258
• /
• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• Journal of Korea Society of Digital Industry and Information Management
• /
• v.8 no.2
• /
• pp.49-58
• /
• 2012

This paper is on an improved orthogonal projection method which can cancel the acoustic feedback signals in the digital hearing aids. Comparing with the NLMS algorithm which is widely used for simplicity and stability, it shows that this method has the improvement of the convergence performances, and has small computational quantities, for signals with the large auto-correlation as speech signals. This uses the improved orthogonal projection algorithm which reduces the correlation of signals. To verify the convergence characteristics of the proposed algorithm, we simulated about various input signals. The acoustic feedback canceller has a 12-bit resolution with 64-tap adaptive FIR filter. And we compared the results of simulation for this algorithm with the ones for the NLMS algorithm. By these works, it is proved that the feedback canceller adopting the proposed algorithm shows about 3.5dB more high SNR than the NLMS algorithm in the colored input signals.

• Communications for Statistical Applications and Methods
• /
• v.27 no.5
• /
• pp.523-533
• /
• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• The Journal of the Acoustical Society of Korea
• /
• v.23 no.3
• /
• pp.221-227
• /
• 2004

This paper presents the subband affine projection algorithm(SAPA). The improved performance of SAPA is achieved by applying the affine projection algorithm to the subband adaptive structure. In this algorithm, the weight updating formula of adaptive filter is simply derived by using the orthogonal quadrature filter(OQF) as an analysis filter bank for subband filtering. The derived SAPA has the fast convergence speed and small computational complexity. The efficiency of the proposed algorithm for colored input signal is evaluated through some experiments.

• Korean Journal of Computational Design and Engineering
• /
• v.18 no.1
• /
• pp.49-57
• /
• 2013

In this paper, orthogonal projection of a point onto a 2D planar curve is discussed. The problem is formulated as finding a point on a curve where the tangent of the curve is perpendicular to the vector connecting the point on the curve and a point in the space. Existing methods are compared and novel approaches to solve the problem are presented. The proposed methods are tested with examples.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2010.11a
• /
• pp.119-120
• /
• 2010

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.43 no.2 s.308
• /
• pp.73-81
• /
• 2006

This paper proposes the improved orthogonal projection method as a new technique advancing the performance of the acoustic echo canceller. Comparing with the widely used NLMS adaptive algorithm which is simple and stable, it shows that this method has the improvement of the convergence speed for signals with the large auto-correlation, and has small computational quantities. In order to testify performances of the orthogonal projection method whom this paper proposes, we have coded a simulation program md executed computer simulations. We observed convergence curves by using two adaptive algorithm for noises and speeches. From simulation results for two input signals, the proposed method shows the high ERLE and the fast convergence and the stable operation in case of using speeches as well as noises.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.9 no.4
• /
• pp.703-711
• /
• 2005

This paper proposes the improved orthogonal projection method as a new technique advancing the performance of the echo cancellation for speeches in the acoustic echo canceller. Comparing with the used NLMS adaptive algorithm, it shows that this method improves the performance of the echo cancellation for signals with the large auto-correlation. In order to testify performances of the orthogonal projection method whom this paper proposes, we have coded a simulation program and executed computer simulations. We observed convergence curves by using two adaptive algorithm for noises and speeches. From simulation results for two input signals, the proposed method shows the high ERLE and the fast convergence and the stable operation in case of using speeches as well as noises.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.16 no.11
• /
• pp.2388-2396
• /
• 2012

This paper is on an simplified orthogonal projection method which cancel the acoustic echo signals in the stereo acoustic echo canceller. Comparing with the NLMS algorithm which is widely used for simplicity and stability, it shows that this method has the improvement of the convergence performances for signals with the high auto-correlation, and has small computational quantities. To verify the convergence characteristics of the proposed algorithm, we simulated about various input signals. And we compared the results of simulation for this algorithm with the ones for the NLMS algorithm. By these works, it was proved that the stereo acoustic echo canceller adopting the proposed algorithm shows about 3dB more high ERLE than the NLMS algorithm for the white noise signals, and 5dB for the colored voice signals.