Saturation effects in active noise control systems

The reference and error sensors of active noise control (ANC) systems will be saturated in real-world applications if the noise level exceeds the dynamic range of the sensors. However, there is a lack of analysis of saturation effects on the performance of ANC systems. This paper proposes an indirect method for analyzing the saturation effects in steady state using Fourier analysis. This indirect method uses clipping to approximate saturation and decomposes the saturated narrowband signal as the summation of a set of rectangular waves and a pulse-amplitude modulated signal. The theoretical analysis shows that the clipping of a sinusoidal signal produces extra odd harmonics, thus affecting the convergence speed and steady-state solution of adaptive filter in ANC systems. This analysis can be extended to narrowband noises that consist of multiple sinusoidal components such as engine noise in many ANC applications. A low-pass filter is effective in reducing saturation effects for harmonic-related noises. Analysis results are verified by computer simulations using recorded engine noise and transfer functions measured from an experimental setup.     

On the development of adaptive hybrid active noise control system for effective mitigation of nonlinear noise

The presence of nonlinearities as well as acoustic feedback deteriorates the cancellation performance of the conventional filtered-x LMS (FxLMS) algorithm based active noise control (ANC) systems. With an objective to improve the performance, a novel filtered-su LMS (FsuLMS) algorithm based ANC system which employs a convex combination of an adaptive IIR filter with a functional link artificial neural network (FLANN) is proposed in this paper. The corresponding learning algorithm of the ANC system is derived and used in the simulation study for performance evaluation. Simulation study reveals enhanced performance of the proposed system over that of its component filters.     

Hybrid filtered error LMS algorithm: another alternative to filtered-x LMS

The filtered-error LMS (FELMS) algorithms are widely used in multi-input and multi-output control (MIMO) active noise control (ANC) systems as an alternative to the filtered-x LMS (FXLMS) algorithms to reduce the computational complexity and memory requirements. However, the available FELMS algorithms introduce significant delays in updating the adaptive filter coefficients that slow the convergence rate. In this paper, we introduce a novel algorithm called the hybrid filtered-error LMS algorithm (HFELMS) which, while still a form of the FELMS algorithm, allows users to have some freedom to construct the error filter that guarantees its convergence with a sufficiently small step size. Without increasing the computational complexity, the proposed algorithm can improve the control system performance in one of several ways: 1) increasing the convergence rate without extra computation cost; 2) reducing the remaining noise mean square error (MSE); or 3) shaping the excess noise power. Simulation results show the effectiveness of the proposed method.     

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method     

Active noise control using an adaptive bacterial foraging optimization algorithm

This paper presents an adaptive bacterial foraging optimization (ABFO) algorithm for an active noise control system. The conventional active noise control (ANC) systems often use the gradient-based filtered-X least mean square algorithms to adapt the coefficients of the adaptive controller. Hence, there is a possibility to converge to local minima. In addition, this class of algorithms needs prior identification of the secondary path. The ABFO algorithm helps the ANC system to prevent falling into local minima. The proposed ANC system is also simpler since it does not need any prior information of the secondary path. Moreover, the adaptive strategy of the algorithm results in improved search performance compared with the basic bacterial foraging optimization algorithm, as well as other conventional algorithms. Experimental studies are performed for nonlinear primary path along with linear and nonlinear secondary path. The results show the effectiveness of the proposed ABFO-based ANC system for different kinds of input noise.     

New nonlinear algorithms for narrowband interference suppression inCDMA spread-spectrum systems

The narrow-band interference suppression capability of spread-spectrum systems can be further enhanced by employing interference suppression filters. This paper proposes a number of new nonlinear algorithms for narrow-band interference suppression in code division multiple access spread-spectrum systems. Our research consists of two parts. (1) We propose a multiuser decision-directed Kalman (MDK) filter, which has the same performance as the nonlinear approximate conditional mean (ACM) filter but a much simpler algorithm. (2) We use the nonlinear function in the ACM and the MDK filters to develop nonlinear adaptive least mean square filters with significantly improved performance. Simulation results indicate that our nonlinear algorithms outperform conventional linear ones     

Adaptive Volterra filters for active control of nonlinear noiseprocesses

This paper presents a Volterra filtered-X least mean square (LMS) algorithm for feedforward active noise control. The research has demonstrated that linear active noise control (ANC) systems can be successfully applied to reduce the broadband noise and narrowband noise, specifically, such linear ANC systems are very efficient in reduction of low-frequency noise. However, in some situations, the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic, white, or tonal noise process, and the primary noise at the canceling point may exhibit nonlinear distortion. Furthermore, the secondary path estimate in the ANC system, which denotes the transfer function between the secondary source (secondary speaker) and the error microphone, may have nonminimum phase, and hence, the causality constraint is violated. If such situations exist, the linear ANC system will suffer performance degradation. An implementation of a Volterra filtered-X LMS (VFXLMS) algorithm based on a multichannel structure is described for feedforward active noise control. Numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered-X LMS algorithm for the following two situations: (1) the reference noise is a nonlinear noise process, and at the same time, the secondary path estimate is of nonminimum phase; (2) the primary path exhibits the nonlinear behavior. In addition, the developed VFXLMS algorithm can also be employed as an alternative in the case where the standard filtered-X LMS algorithm does not perform well     

Feedforward adaptive noise control with multivariable gradientlattice filters

This work presents a novel feedforward adaptive noise control (ANC) algorithm based on multivariable gradient lattice filters to control acoustic noise or vibration globally. In addition, a gradient-based lattice for AR and FIR models and its transpose lattice for the multivariable ANC algorithm are derived. The filter has different forward and backward reflection coefficient matrices to provide a faster convergence than the gradient lattice algorithm when using the same reflection coefficient matrices. Experimental results demonstrate the effectiveness of the proposed algorithm in controlling broadband acoustic noise in an enclosure     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results.     

A new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control systems

Infinite impulse response filters have not been used extensively in active noise and vibration control applications. The problems are mainly due to the multimodal error surface and instability of adaptive IIR filters used in such applications. Considering these, in this paper a new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control applications is proposed. At first an RLS-based adaptive IIR filter with computational complexity of order O(n²) is derived, and a sufficient condition for its stability is proposed by applying passivity theorem on the equivalent feedback representation of this adaptive algorithm. In the second step, to reduce the computational complexity of the algorithm to the order of O(n) as well as to improve its numerical stability, a fast array implementation of this adaptive IIR filter is derived. This is accomplished by extending the existing results of fast-array implementation of adaptive FIR filters to adaptive IIR filters. Comparison of the performance of the fast-array algorithm with that of Erikson’s FuLMS and SHARF algorithms confirms that the proposed algorithm has faster convergence rate and ability to reach a lower minimum mean square error which is of great importance in active noise and vibration control applications.     

Design and performance of adaptive systems based on structured stochastic optimization strategies

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to MR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the particle swarm optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.     

Active control of nonlinear noise processes in a linear duct

This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller     

自适应加权FIR-Myriad混合滤波算法

针对FIR滤波器滤除脉冲噪声以及加权Myriad滤波器滤除高斯噪声的不足,提出基于FIR滤波器和加权WMy滤波器有效组合的一类新的非线性滤波器FIR-WMyH滤波器.利用神经网络中的反向传播算法,在均方误差准则下,推导了一个基于统计梯度的自适应算法.基于稳定α分布脉冲噪声模型下的仿真结果说明了该算法的良好的性能.     

Adding explicit content classification to nonlinear filters

Nonlinear filters are known for better edge-preserving performance in image processing applications as they can adapt to some local image content. Instead of trying to find a single optimal filter that can adapt to all the image content, some classification-based approaches first apply a pre-classification on the image content and then employ an optimal linear filter for each content class. It is interesting to extend the linear filter in such approaches to a nonlinear filter and see if the explicit content classification, can still add to such inherently adapting nonlinear filters. In this paper, we investigate several categories of nonlinear filters: order statistics filters, hybrid filters, neural filters, and bilateral filters with different forms of content classification in various image processing applications, including image de-blocking, noise reduction, and image interpolation.     

A tree-structured piecewise linear adaptive filter

The authors propose and analyze a novel architecture for nonlinear adaptive filters. These nonlinear filters are piecewise linear filters obtained by arranging linear filters and thresholds in a tree structure. A training algorithm is used to adaptively update the filter coefficients and thresholds at the nodes of the tree, and to prune the tree. The resulting tree-structured piecewise linear adaptive filter inherits the robust estimation and fast adaptation of linear adaptive filters, along with the approximation and model-fitting properties of tree-structured regression models. A rigorous analysis of the training algorithm for the tree-structured filter is performed. Some techniques are developed for analyzing hierarchically organized stochastic gradient algorithms with fixed gains and nonstationary dependent data. Simulation results show the significant advantages of the tree-structured piecewise linear filter over linear and polynomial filters for adaptive echo cancellation     

An adaptive noise canceller with low signal distortion for speechcodecs

This paper proposes an adaptive noise canceller (ANC) with low signal distortion for speech codecs. The proposed ANC has two adaptive filters: a main filter (MF) and a subfilter (SF). The signal-to-noise ratio (SNR) of input signals is estimated using the SF. To reduce signal distortion in the output signal of the ANC, a step size for coefficient update in the MF is controlled according to the estimated SNR. Computer simulation results using speech and diesel engine noise recorded in a special-purpose vehicle show that the proposed ANC reduces signal distortion in the output signal by up to 15 dB compared with a conventional ANC. Results of subjective listening tests show that the mean opinion scores (MOSs) for the proposed ANC with and without a speech codec are one point higher than the scores for the conventional ANC     

噪声有源控制的人工神经网络方法

讨论了有源噪声控制（ＡＮＣ）问题,提出一种基于人工神经网络的非线性噪声有源自适应控制方法,给出了一种基于误差梯度下降的学习算法,证明了闭环控制系统在Ｌｙａｐｕｎｏｖ意义下的稳定性。     

Nonlinear techniques for interference suppression inspread-spectrum systems

The binary nature of direct-sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose. The case of a Gaussian interferer with known autoregressive parameters is considered. Using simulations, it is shown that an approximate conditional mean (ACM) filter of the Masreliez type performs significantly better than the optimum linear (Kalman-Bucy) filter. For the case of interferers with unknown parameters, the nature of the nonlinearity in the ACM filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction. Two versions of this filter are considered: one in which the filter coefficients are updated using the Widrow LMS algorithm, and another in which the coefficients are updated using an approximate gradient algorithm. Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer     

A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.