• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.5
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• pp.410-416
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• 2003

In the affine projection algorithm(APA), the projection dimension depends on a number of projection basis and of elements of input vector used for updating of coefficients of the adaptive filter. The projection dimension is closely related to a convergence speed of the APA, and it determines computational complexity. As the adaptive filter approaches to steady state, convergence speed is decreased. Therefore it is possible to reduce projection dimension that determines convergence speed. In this paper, we proposed the variable dimension affine projection algorithm (VDAPA) that controls the projection dimension and uses the relation between variations of coefficients of the adaptive filter and convergence speed of the APA. The proposed method reduces computational complexity of the APA by modifying the number of projection basis on convergence state. For demonstrating the good performances of the proposed method, simulation results are compared with the APA and normalized LMS algorithm in convergence speed and computational quantity.

• The Journal of the Acoustical Society of Korea
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• v.26 no.2
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• pp.69-74
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• 2007

In signal processing applications with highly correlated input signals, subband affine projection algorithm and step size controlling is a good solution for improving the slow convergence rate and large computational complexity of LMS-type algorithms. This paper proposes a subband affine projection algorithm using a variable step size. The proposed method achieves fast convergence rate and small steady-state error with a small computational complexity by combining the SAP and step size controlling in a subband structure. Experimental results on highly correlated input signal show that the proposed method is superior to the conventional methods.

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

• The Journal of the Acoustical Society of Korea
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• v.31 no.2
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• pp.79-86
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• 2012

In this paper, we propose an enhanced algorithm for affine projection algorithms which have been proposed to speed up the convergence of the conventional NLMS algorithm. Since affine projection (AP) or pseudo AP algorithms are based on the delayed input vector and error vector, they are complicated and not suitable for applying methods developed for the LMS-type algorithms which are based on the scalar error signal. We devised a variable step size algorithm for pseudo AP using the fact that pseudo AP algorithms are updated using the scalar error and that the error signal is getting orthogonal to the input signal. We carried out a performance comparison of the proposed algorithm with other pseudo AP algorithms using a system identification model. It is shown that the proposed algorithm presents good convergence characteristics under both stationary and non-stationary environments despites its low complexity.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.6
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• pp.163-174
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• 2009

Applying the maximally polyphase decomposition and noble identity to the adaptive filter in subband structure, the conventional fullband affine projection algorithm is translated to the subband affine projection (SAP) algorithm. The Maximally polyphase decomposed SAP (MPDSAP) algorithm is a special version of the SAP algorithm, and its adaptive sub-filters have unity projection dimension. The weight updating formular of the MPDSAP is similar to that of the NLMS algorithm, so it may be more proper algorithm than other AP-type algorithms for many practical applications. This paper presents a new statistical analysis of the MPDSAP algorithm. The analytical model is derived for autoregressive (AR) inputs and the nonunity adaptive gain in the subband structure with the orthonormal analysis filters (OAF), The pre-whitening by the OAF allows the derivation of a simple-analytical model for the MPDSAP with the AR inputs and the nonunity adaptive gain.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.5 s.305
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• pp.145-156
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• 2005

In application for acoustic echo cancellation and adaptive equalization, input signal is highly correlated and the long length of adaptive filter is needed. Affine projection algorithms, in these applications, can produce a good convergence performance. However, they have a drawback that is a complex hardware implementation. In this paper, we propose a new subband affine projection algorithm with improved convergence and reduced computational complexity. In addition, we suggest a good approach to implement the proposed method. In this method by applying polyphase decomposition, noble identity and critical decimation to the anne projection algorithm the number of input vectors for decorrelation can be reduced. The weight-updating formula of the proposed method is derived as a simple form that compared with the NLMS(normalized least mean square) algorithm by the reduced projection order The efficiency of the proposed algorithm for a colored input signal was evaluated by using computer simulations.

• The Journal of the Acoustical Society of Korea
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• v.33 no.6
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• pp.420-426
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• 2014

In this paper, we propose a new affine projection sign algorithm (APSA) to improve the convergence speed of the conventional APSA which has been proposed to enable the affine projection algorithm (APA) to operate robustly in impulsive noise environment. The conventional APSA has two advantages; it operates robustly against impulsive noise and does not need calculation for the inverse matrix. The proposed algorithm also has the conventional algorithm's advantages and furthermore, better convergence speed than the conventional algorithm. In the conventional algorithm, each input signal is normalized by $l_2$-norm of all input signals, but the proposed algorithm uses input signals normalized by their corresponding $l_2$-norm. We carried out a performance comparison of the proposed algorithm with the conventional algorithm using a system identification model. It is shown that the proposed algorithm has the faster convergence speed than the conventional algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.3
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• pp.443-448
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• 2022

This paper presents a subband affine projection algorithm with variable step size to improve convergence performance in adaptive filtering applications with long adaptive filters and highly correlated input signals. The proposed algorithm can obtain fast convergence speed and small steady-state error by using different step sizes for each adaptive sub-filter in the subband structure to which polyphase decomposition and noble identity are applied. The step size derived to minimize the mean square error of the adaptive filter at each update time shows better convergence performance than the existing algorithm using a variable step size. In order to confirm the convergence performance of the proposed algorithm, which is superior to the existing algorithm, computer simulations are performed for mean square deviation(MSD) for AR(1) and AR(2) colored input signals considering the system identification model.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.11
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• pp.1545-1550
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• 2021

We propose an optimal variable step size adjustment method for the simplified subband affine projection algorithm (Simplified SAP; SSAP) in a subband structure based on a polyphase decomposition technique. The proposed method provides an optimal step size derived to minimize the mean square deviation(MSD) at the time of updating the coefficients of the subband adaptive filter. Application of the proposed optimal step size in the SSAP algorithm using colored input signals ensures fast convergence speed and small steady-state error. The results of computer simulations performed using AR(2) signals and real voices as input signals prove the validity of the proposed optimal step size for the SSAP algorithm. Also, the simulation results show that the proposed algorithm has a faster convergence rate and good steady-state error compared to the existing other adaptive algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.5A
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• pp.717-725
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• 2000

Within the last several years, there has been a large number of algorithms developed for face recognition. The majority of these algorithms have been view- and projection-based algorithms. Our definition of projection is not restricted to projecting the image onto an orthogonal basis the definition is expansive and includes a general class of linear transformation of the image pixel values. The class includes correlation, principal component analysis, clustering, gray scale projection, and matching pursuit filters. In this paper, we perform a detailed analysis of this class of algorithms by evaluating them on the FERET database of facial images. In our experiments, a projection-based algorithms consists of three steps. The first step is done off-line and determines the new basis for the images. The bases is either set by the algorithm designer or is learned from a training set. The last two steps are on-line and perform the recognition. The second step projects an image onto the new basis and the third step recognizes a face in an with a nearest neighbor classifier. The classification is performed in the projection space. Most evaluation methods report algorithm performance on a single gallery. This does not fully capture algorithm performance. In our study, we construct set of independent galleries. This allows us to see how individual algorithm performance varies over different galleries. In addition, we report on the relative performance of the algorithms over the different galleries.