$$L_{1}$$-norm constrained normalized subband adaptive filter algorithm with variable norm-bound parameter and improved version

The \(L_{1}\)-norm constrained normalized subband adaptive filter with variable norm-bound parameter \((L_{1}\hbox {NCNSAF-V})\) algorithm and its variable step size version VSS-\(L_{1}\)NCNSAF-V are proposed in this paper, which are more superior to some existing algorithms in the sparse system. The proposed \(L_{1}\)NCNSAF-V is derived by using the Lagrange multiplier method, and the VSS-\(L_{1}\)NCNSAF-V is obtained by minimizing the statistical square of the Euclidean norm of the noise-free subband a posterior error vector. The simulation results demonstrate that the proposed algorithms achieve good performance.     

Steady-state behavior of the improved normalized subband adaptive filter algorithm and its improvement in under-modeling

In practice, adaptive filter could work in an under-modeling scenario, meaning that its length is less than that of the unknown system. In this realistic situation, therefore, the existing analysis for the improved normalized subband adaptive filter (INSAF) algorithm is not applicable. To this end, this paper analyzes the mean square steady-state performance of the INSAF for under-modeling. In addition, we propose a variable step size INSAF algorithm suitable for under-modeling scenario, to obtain fast convergence rate and low steady-state error. Simulation results have supported our theoretical analysis and proposed algorithm.     

A joint-optimization NSAF algorithm based on the first-order Markov model

Recently, the normalized subband adaptive filter (NSAF) algorithm has attracted much attention for handling colored input signals. Based on the first-order Markov model of the optimal weight vector, this paper provides some insights for the convergence of the standard NSAF. Following these insights, both the step size and the regularization parameter in the NSAF are jointly optimized by minimizing the mean-square deviation. The resulting joint-optimization step size and regularization parameter algorithm achieves a good tradeoff between fast convergence rate and low steady-state error. Simulation results in the context of acoustic echo cancelation demonstrate good features of the proposed algorithm.     

Analysis of a sign algorithm with delayed data

An adaptive filter whose weights are adapted using a sign algorithm with a delayed error signal is analyzed. For stationary environments it is proved that the excess average absolute estimation error is bounded for all values of the error signal delay and the algorithm step size. For the nonstationary case when the optimal filter weights are time varying, the optimum step size which minimizes the excess average absolute error is derived. It is shown that the optimum step size does not depend on the additive noise power. The analytical results are supported by computer simulations     

Adaptive Combination of Proportionate NSAF with the Tap-Weights Feedback for Acoustic Echo Cancellation

To obtain fast convergence rate and low steady-state error in acoustic echo cancellation, a convex combination scheme of the improved proportionate normalized subband adaptive filter algorithm is proposed. Instead of the gradient method in the conventional combination theory, the mixing parameter is adapted by using the normalized gradient method which makes it more robust to the variations of subband error signals. Also, to implement a smooth transition from the fast filter to the accurate filter, a cyclic feedback of the overall tap-weights giving to all component filters is applied.     

A variable step size LMS algorithm

A least-mean-square (LMS) adaptive filter with a variable step size is introduced. The step size increases or decreases as the mean-square error increases or decreases, allowing the adaptive filter to track changes in the system as well as produce a small steady state error. The convergence and steady-state behavior of the algorithm are analyzed. The results reduce to well-known results when specialized to the constant-step-size case. Simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual LMS algorithm and another variable-step-size algorithm. They show that its performance compares favorably with these existing algorithms     

一种变正则化矩阵的改进多带结构子带自适应滤波算法

定正则化因子的改进多带结构子带自适应滤波(IMSAF)算法在取得收敛速度快和稳态失调误差小之间存在冲突.根据系统噪声抵消原理,设定子带后验误差功率等于子带噪声功率,本文提出了变正则化矩阵的IMSAF算法来解决这一问题.仿真结果证明,所提算法可以同时达到收敛速度快、稳态失调误差小以及追踪速度快等优势.     

A stochastic gradient adaptive filter with gradient adaptive stepsize

The step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration. An approximate analysis of the performance of the adaptive filter when its inputs are zero mean, white, and Gaussian noise and the set of optimal coefficients are time varying according to a random-walk model is presented. The algorithm has very good convergence speed and low steady-state misadjustment. The tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square (LMS) algorithm for a large range of values of the step size of the adaptation algorithm. Several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented     

基于多相滤波器组的非线性回声抵消

在免提通话系统和移动通信设备中，扬声器常常工作在较高的音量下，容易发生过载现象，从而产生明显的非线性声学回声，这在小微型扬声器中更加常见。常用的线性AEC(Acoustic Echo Cancellation)算法无法消除此类非线性回声，因此通话质量受到严重影响。非线性回声主要表现为额外的高频谐波分量，这些分量使得全带系统不再满足线性关系，而通常的AEC算法都是基于最小化全带误差推导而来，因此性能很容易受到非线性失真的影响。本文提出了一种基于多相滤波器组的子带AEC算法，把全带误差变成了各个子带的误差，因而把谐波失真成分变成了某些子带内的加性噪声，这使得谐波失真较小的那些子带依然能够正常收敛。通过仿真和实测实验，当出现非线性失真时，新方法的ERLE(Echo Return Loss Enhancement)明显高于经典的全带时域和频域方法，对于非线性失真明显的语音信号，ERLE提升约10 dB。      

A Modular Analog NLMS Structure for Adaptive Filtering

This paper proposes a modular Analog Adaptive filter (AAF) algorithm, in which the coefficient adaptation is carried out by using a time varying step size analog normalized LMS (NLMS) algorithm, which is implemented as an external analog structure. The proposed time varying step size is estimated by using the first element of the crosscorrelation vector between the output error and reference signal, and the first element of the crosscorrelation vector between the output error and the adaptive filter output signal, respectively. Proposed algorithm reduces distortion when additive noise power increases or DC offsets are present, without significatively decreasing the convergence rate nor increasing the complexity of the conventional NLMS algorithms. Simulation results show that proposed algorithm improves the performance of AAF when DC offsets are present. The proposed VLSI structure for the time varying step size normalized NLMS algorithm has, potentially, a very small size and faster convergence rates than its digital counterparts. It is suitable for general purpose applications or oriented filtering solution such as echo cancellation and equalization in cellular telephony in which high performance, low power consumption, fast convergence rates and small size adaptive digital filters (ADF) are required. The convergence performance of analog adaptive filters using integrators like first order low pass filter is analyzed.     

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising.

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.     

利用直接矩阵求逆和临界采样子带自适应滤波器的快速系统辨识

在许多应用中,子带自适应滤波器结构已经显示了其在计算和性能上的优点。基于最近提出的一个采用临界采样滤波器组的子带自适应结构,该文引入了子带直接矩阵求逆(DMI)算法。在保持了该算法快速收敛优点的同时,利用相关矩阵块三对角的特殊结构,降低了该算法的计算复杂度。理论分析及计算机实验显示,子带直接矩阵求逆算法只需经过较少的更新次数自适应子滤波器自由度的两倍,就能够收敛到高于最小均方误差的3dB附近。     

Nonuniform Subband Adaptive Filtering With Critical Sampling

Adaptive subband structures have been proposed with the objective of increasing the convergence speed and/or reducing the computational complexity of conventional adaptive algorithms, mainly for applications that require a large number of adaptive coefficients. In this paper, we present a nonuniform subband structure with critical sampling, which is capable of modeling an arbitrary finite-impulse response (FIR) system with reduced aliasing. A least-mean-square (LMS)-type adaptation algorithm with normalized step sizes, which works at the lowest downsampling rate and minimizes the average of the subband squared errors, is derived for the proposed structure. A convergence analysis of the adaptation algorithm is presented, from which its convergence rate and steady-state mean-square error can be estimated.     

一种约束稳定性最小均方噪声对消算法

研究了最小均方误差(LMS)算法、归一化的最小均方(NLMS)算法及变步长NLMS算法在自适应噪声干扰抵消器中的应用,针对目前这些算法在噪声对消器应用中的缺点,将约束稳定性最小均方(CS-LMS)算法应用到噪声处理中,并进一步结合变步长的思想提出来一种新的变步长CS-LMS算法。通过MATLAB进行仿真分析,结果证实提出的算法与其他算法相比,能很好地滤除掉噪声从而得到期望信号,明显的降低了稳态误差,并拥有好的收敛速度。     

Subband adaptive filtering with real-valued subband signals foracoustic echo cancellation

Adaptive filtering in subbands was originally proposed to overcome the limitations of conventional least-mean-square (LMS) algorithms. In general, subband adaptive filters offer computational savings, as well as faster convergence over the conventional LMS algorithm. However, improvements to current subband adaptive filters could be further enhanced by a more elegant choice of their design/structure. Classical subband adaptive filters employ DFT-based analysis and synthesis filter banks which results in subband signals that are complex-valued. The authors modify the structure of subband adaptive filters by using single-sideband (SSB) modulated analysis and synthesis filter banks, which result in subband signals that are real-valued. This simplifies the realisation of subband adaptive filters     

Improved stochastic gradient adaptive filter with gradient adaptivestep size

The performance of a stochastic gradient adaptive filter can be significantly improved by introducing a forgetting factor. The complexity of the original algorithm can also be reduced by using only the signs of error signals and input signals in the gradient adaptive step size computation     

一种类箕舌线函数的变步长归一化自适应滤波算法

在综合考虑自适应滤波算法设计中收敛速度、稳态误差、计算复杂度和跟踪性能等指标的基础上,该文提出一种类箕舌线函数的变步长归一化自适应滤波算法,用类箕舌线函数代替Sigmoid函数作为步长迭代公式,引入基于相关误差的变步长调整原则,在大大增强算法稳定性的同时大幅度提升了算法的收敛速度、跟踪性能,减小了算法的计算复杂度。在Matlab平台上分析了改进的步长函数中参数\begin{document}$\alpha $\end{document},以及的不同取值对算法的影响,并将该文算法与已有的基于Sigmoid函数和基于箕舌线函数的变步长LMS算法进行了比较,仿真结果表明,该文算法有更快的收敛速度、更好的跟踪能力以及较小的稳态误差和较强的鲁棒性。     

变抽头长度LMS自适应滤波算法

该文将自适应滤波器抽头长度与权值调整问题归结为单一的权值调整问题,提出了抽头长度的一般更新公式及新的变抽头长度LMS算法,从理论上分析了其合理性与收敛性。新算法用长滤波器与短滤波器的时平均平方误差估计稳态均方误差,采用了自适应调整的抽头长度步长,可在滤波器权值未收敛时就快速更新抽头长度。论文还证明了目前文献中几种有效的变抽头长度算法也可看作或化为文中抽头长度一般更新公式的特例,理论分析与自适应系统辨识的仿真结果验证了新算法的有效性。     

Delayless subband adaptive filtering using the Hadamard transform

In this correspondence, an analysis of a delayless critically decimated subband adaptive filter structure is presented. In this structure, adaptive weights in each subband are computed by the LMS algorithm and then transformed into those in fullband by the Hadamard transform. It is shown that a stationary point of the proposed algorithm corresponds to the fullband Wiener filter. Some numerical results are also presented to show the performance of this scheme     

Analysis of the frequency domain adaptive filter

The purpose of this note is to demonstrate significant analytical simplifications for studying the behavior of adaptive filtering in the frequency domain as opposed to studying the behavior of adaptive filtering in the time domain. A closed form expression, for the single complex weight in the frequency domain adaptive filter, is presented which allows significant statistical analysis to be performed. The mean-square error of the filter is evaluated as a function of the algorithm step size and the signal and noise powers.