Normalized Subband Adaptive Filter Research Articles

Selective Normalized Subband Adaptive Filter With Subband Extension

We present a novel subband adaptive filtering (SAF) algorithm that selects a subset of subbands and uses them to update the adaptive filter weight. The normalized SAF (NSAF) algorithm has a tradeoff between the number of subbands and the convergence speed. As the number of subbands increases, the convergence speed gets faster. However, employing an increased number of subbands raises the computational complexity. To improve the convergence speed, we first extend the number of subbands and then develop a selective scheme exploiting an efficient subset of the extended subbands so as to remove redundancy in the computational complexity. We show that subbands with a larger ratio of the corresponding squared error to an input power should be selected to achieve a similar performance to that of the extended subband adaptive filter. Experimental results show that the proposed NSAF algorithm has better convergence performance compared with the conventional NSAF algorithm.

Subband Adaptive Filtering withl1-Norm Constraint for Sparse System Identification

This paper presents a new approach of the normalized subband adaptive filter (NSAF) which directly exploits the sparsity condition of an underlying system for sparse system identification. The proposed NSAF integrates a weightedl1-norm constraint into the cost function of the NSAF algorithm. To get the optimum solution of the weightedl1-norm regularized cost function, a subgradient calculus is employed, resulting in a stochastic gradient based update recursion of the weightedl1-norm regularized NSAF. The choice of distinct weightedl1-norm regularization leads to two versions of thel1-norm regularized NSAF. Numerical results clearly indicate the superior convergence of thel1-norm regularized NSAFs over the classical NSAF especially when identifying a sparse system.

Enhanced Normalized Subband Adaptive Filter with Variable Step Size

본 논문에서는 전밴드(full-band) 적응 필터의 수렴 특성을 개선하기 위해 제안된 정규 부밴드 적응 필터(NSAF)의 성능을 향상시키기 위한 가변 스텝 사이즈 기반의 알고리즘을 제안하였다. 널리 알려진 Kwong의 가변 스텝 사이즈 적응 필터는 간단한 하면서도, 고정된 스텝 사이즈의 적응 필터에 비하여 우수한 성능을 보인다. 그러나 가산잡음이 클 경우, 잡음의 크기에 비례하여 성능이 저하되는 단점이 있다. 본 논문에서는 적응 오차에서 추정된 가산 잡음을 차감한 정규 오차를 이용함으로써 가산 잡음에 의존하지 않는 가변 스텝 사이즈 알고리즘을 제안하였다. 시스템 확인 모델 하에서 컴퓨터 모의 실험을 통하여 제안된 알고리즘이 기존의 알고리즘들에 비하여 정상 및 비정상 환경에서 수렴 특성이 우수함을 보였다. In this paper, we propose a variable step size algorithm to enhance the normalized subband adaptive filter which has been proposed to improve the convergence characteristics of the conventional full band adaptive filter. The well-known Kwong's variable step size algorithm is simple, but shows better performance than that of the fixed step size algorithm. However, in case that large additive noise is present, the performance of Kwong's algorithm is getting deteriorated in proportion to the amount of the additive noise. We devised a variable step size algorithm which does not depend on the amount of additive noise by exploiting a normalized adaptation error which is the error subtracted and normalized by the estimated additive noise. We carried out a performance comparison of the proposed algorithm with other algorithms using a system identification model. It is shown that the proposed algorithm presents good convergence characteristics under both stationary and non-stationary environments.

A Variable Step Size for Normalized Subband Adaptive Filters

A normalized subband adaptive filter algorithm uses a fixed step size, which is chosen as a trade-off between the steady-state error and the convergence rate. In this letter, a variable step size for normalized subband adaptive filters is derived by minimizing the mean-square deviation between the optimal weight vector and the estimated weight vector at each instant of time. The variable step size is presented in terms of error variance. Therefore, the proposed algorithm is capable of tracking in non-stationary environments. The simulation results show good tracking ability and low misalignment of the proposed algorithm in system identification.

A Low Complexity NSAF Algorithm

This letter proposes a novel normalized subband adaptive filter (NSAF) algorithm, which applies variable step sizes to subband filters to improve the convergence performance of the conventional NSAF and update only a subset of the subbands per iteration to reduce its computational complexity. The selection process for each subband is based on the amount of improvement it makes to the mean square deviation at every iteration. Simulation results show significant reduction in computational complexity, faster convergence rate, and lower misadjustment error achieved using the proposed scheme.

Noise-robust normalised subband adaptive filtering

Proposed is a robust normalised subband adaptive filter (NSAF) for identifying a highly noisy system. The proposed NSAF reutilises a number of past weight vectors in adaptation, whereas the classical NSAF relies only on the immediately previous weight vector. A new constrained optimisation criterion is formulated so as to minimise the sum of the squared Euclidean norms of the changes between the weight vectors to be updated and the past weight vectors. The resultant NSAF exhibits robustness to noise in that it prevents the adaptive filter from fluctuating around an optimal solution. Through experiments, the proposed NSAF shows lower steady-state misalignment than the conventional NSAF while retaining comparable convergence rate, especially when noise gets severe.

Normalised subband adaptive filter with variable step size

Proposed is a normalised subband adaptive filter algorithm with a variable step size based on the mean-square deviation (MSD) analysis. Since the spectrum of each input signal in subbands is close to that of white noise, the MSD can be approximated. The step size in this study is chosen such that the MSD undergoes the largest decrease from one iteration to the next, which leads to a fast convergence rate and a small misalignment. Simulation results confirm that the proposed algorithm outperforms existing algorithms in the literature.

Improved normalised subband adaptive filter

Proposed is a subband adaptive filter, which is derived by minimising the sum of the squared Euclidean norms of the differences between the updated tap-weight vector and past tap-weight vectors subject to a set of constraints on the updated tap-weight vector of the adaptive filter. Simulation results show that the misalignment of the proposed subband adaptive filter is low in a relatively high background noise environment.

Stochastic Analysis of the Normalized Subband Adaptive Filter Algorithm

This paper studies the statistical behavior of the normalized subband adaptive filtering (NSAF) algorithm. An accurate statistical model of the NSAF algorithm is obtained. In the derivation, we focus on Gaussian correlated input signals. By assuming that the analysis filter bank is paraunitary and taking into account the full band adaptation mechanism of the NSAF, expressions for the first and the second moments of the adaptive filter weights are derived without invoking the slow adaptation assumption. In the derivations, several hyperelliptic integrals appear. To tackle those integrals induced by Gaussian correlated inputs, we first give a solution by resorting to the adaptive Lobatto quadrature. By invoking the averaging principle, two other approximation methods, the chi-square method and the partial fraction expansion method, are presented to approximate the statistical model as well. Monte Carlo (MC) simulation results corroborate our predictions. The Lobatto quadrature method achieves a good agreement with the MC simulation results, even for a relatively large step size. Compared with the chi-square method and the partial fraction expansion method, the Lobatto quadrature method gives better performance in terms of predicting the mean square error when the length of the adaptive filters is small to medium. The chi-square approximation method and the partial fraction expansion method give a satisfactory performance with a relatively low computational complexity when the filter length is large.

An Improved Subband Adaptive Filter for Acoustic Echo Cancellation Application

Subband adaptive filters (SAFs) play an important role in digital signal processing field. We propose an improved subband adaptive filter which can be used to remove echo in telephone communication. The presented structure is based on polyphase decomposition of the filter to be integrated with Kalman filtering strategy. Compared to the Normalized Subband adaptive filter(NSAF) algorithm, the novel algorithm exhibits faster convergence when Kalman filtering algorithm is utilized for coefficient updating. Furthermore, with an increased number of subbands in the filter, the convergence rate improves considerably. The efficacy of the proposed algorithm is examined and validated by mathematical analysis and simulation.

A family of proportionate normalized subband adaptive filter algorithms

Abstract In this paper, the concept of proportionate adaptation is extended to the normalized subband adaptive filter (NSAF), and seven proportionate normalized subband adaptive filter algorithms are established. The proposed algorithms are proportionate normalized subband adaptive filter (PNSAF), μ ‐law PNSAF (MPNSAF), improved PNSAF (IPNSAF), the improved IPNSAF (IIPNSAF), the set-membership IPNSAF (SM-IPNSAF), the selective partial update IPNSAF (SPU-IPNSAF), and SM-SPU-IPNSAF which are suitable for sparse system identification in network echo cancellation. When the impulse response of the echo path is sparse, the PNSAF has initial faster convergence than NSAF but slows down dramatically after initial convergence. The MPNSAF algorithm has fast convergence speed during the whole adaptation. The IPNSAF algorithm is suitable for both sparse and dispersive impulse responses. The SM-IPNSAF exhibits good performance with significant reduction in the overall computational complexity compared with the ordinary IPNSAF. In SPU-IPNSAF, the filter coefficients are partially updated rather than the entire filter at every adaptation. In SM-SPU-IPNSAF algorithm, the concepts of SM and SPU are combined which leads to a reduction in computational complexity. The simulation results show good performance of the proposed algorithms.

Selective partial update and set‐membership improved proportionate normalized subband adaptive filter algorithms

AbstractIn this article, the concept of proportionate adaptation is extended to the selective partial update (SPU) and set‐membership (SM) normalized subband adaptive filters (NSAFs), and three proportionate normalized subband adaptive filter algorithms are established. The proposed algorithms are the improved proportionate NSAF (IPNSAF), the SPU improved proportionate NSAF (SPU‐IPNSAF), and the SM‐IPNSAF which are suitable for sparse system identification. When the impulse response of the echo path is sparse, the IPNSAF algorithm has faster convergence than NSAF. The performance of IPNSAF is also suitable for dispersive impulse responses. In SPU‐IPNSAF, the filter coefficients are partially updated rather than the entire filter at every adaptation which reduces the computational complexity of IPNSAF. The SM‐IPNSAF exhibits good performance with significant reduction in the overall computational complexity compared with the ordinary IPNSAF. The simulation results show good performance of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.

A Variable Step-Size Matrix Normalized Subband Adaptive Filter

The normalized subband adaptive filter (NSAF) presented by Lee and Gan can obtain faster convergence rate than the normalized least-mean-square (NLMS) algorithm with colored input signals. However, similar to other fixed step-size adaptive filtering algorithms, the NSAF requires a tradeoff between fast convergence rate and low misadjustment. Recently, a set-membership NSAF (SM-NSAF) has been developed to address this problem. Nevertheless, in order to determine the error bound of the SM-NSAF, the power of the system noise should be known. In this paper, we propose a variable step-size matrix NSAF (VSSM-NSAF) from another point of view, i.e., recovering the powers of the subband system noises from those of the subband error signals of the adaptive filter, to further improve the performance of the NSAF. The VSSM-NSAF uses an effective system noise power estimate method, which can also be applied to the under-modeling scenario, and therefore need not know the powers of the subband system noises in advance. Besides, the steady-state mean-square behavior of the proposed algorithm is analyzed, which theoretically proves that the VSSM-NSAF can obtain a low misadjustment. Simulation results show good performance of the new algorithm as compared to other members of the NSAF family.

Adaptive combination of subband adaptive filters for acoustic echo cancellation

In hands-free telephones and teleconferencing systems, acoustic echo cancellers are required, which are often implemented by adaptive filters. In these applications, the speech input signal of the adaptive filter is highly correlated and the impulse response of the echo path is very long. These characteristics will slow down the convergence rate of the adaptive filter if the well-known normalized least-mean-square (NLMS) algorithm is used. The normalized subband adaptive filter (NSAF) offers a good solution to this problem because of its decorrelating property. However, similar to the NLMS-based adaptive filter, the NSAF requires a tradeoff between fast convergence rate and small steady-state mean-square error (MSE). In this paper, we propose an adaptive combination scheme to address this tradeoff. The combination is carried out in subband domain and the mixing parameter that controls the combination is adapted by means of a stochastic gradient algorithm which employs the sum of squared subband errors as the cost function. The performance of the proposed combination scheme is evaluated in the context of acoustic echo cancellation (AEC). Experimental results show that the combination scheme can obtain both fast convergence rate and small steady-state MSE.

A Subband Adaptive Filtering Algorithm Employing Dynamic Selection of Subband Filters

We present a novel normalized subband adaptive filter (NSAF) which dynamically selects subband filters in order to reduce computational complexity while maintaining convergence performance of conventional NSAF. The selection operation is performed to achieve the largest decrease between the successive mean square deviations at every iteration. As a result, an efficient and competent NSAF algorithm is derived. The experimental results show that the proposed NSAF algorithm gains an advantage over the conventional NSAF in that it leads to a similar convergence performance with a substantial saving of overall computational burden.

Normalised subband adaptive filter with new variable regularisation matrix

A new variable regularisation matrix (VRM) for the normalised subband adaptive filter (NSAF) is proposed, which is derived by letting the powers of the subband a posteriori errors of the NSAF equal the powers of the corresponding subband system noises. Simulation results show that the misalignment of the proposed VRM-NSAF is smaller than that of the authors' previous VRM-NSAF.

A Variable Regularization Matrix Normalized Subband Adaptive Filter

The normalized subband adaptive filter (NSAF) proposed by Lee and Gan is promising. However, there exists the conflicting requirement of fast convergence rate and low misadjustment for the NSAF. In this letter, we propose a variable regularization matrix NSAF (VRM-NSAF) to address this problem. The optimal selection of the regularization matrix is derived by the largest decrease of the mean-square deviation (MSD). Simulation results comparing the proposed VRM-NSAF with the original NSAF are presented to show the advantage of this method, including both fast convergence rate and low misadjustment.

Proportionate normalized subband adaptive filter algorithms for sparse system identification

In this paper, the concept of proportionate adaptation is extended to the normalized subband adaptive filters (NSAFs) and four proportionate adaptive filters are established. The proposed algorithms are proportionate normalized subband adaptive filter (PNSAF), μ -law PNSAF (MPNSAF), improved PNSAF (IPNSAF), and improved IPNSAF (IIPNSAF) which are suitable for sparse system identification. Simulation results show good performance of the proposed algorithms.

Inherent Decorrelating and Least Perturbation Properties of the Normalized Subband Adaptive Filter

This correspondence describes and analyzes a class of subband adaptive filters (SAFs) that stems from various approaches of applying subband and multirate techniques in adaptive filtering. This class of SAFs, called the normalized SAF (NSAF), has a unique weight-control mechanism, whereby subband error signals are used to adapt a fullband tap-weight vector. In this correspondence, we elaborate on the inherent decorrelating properties of the NSAF, which manifest themselves in different forms as integral elements of the weight-control mechanism. We also show that the NSAF possesses some least perturbation properties that are also found in the normalized least-mean-square (NLMS) and affine projection (AP) algorithms