Noise Control Filter Research Articles

Analysis of nonminimum phase components of noise control filters in active noise control

In the active noise control (ANC), it is known that the optimal filter becomes a noncausal filter due to the effect of the nonminimum phase components of the secondary path. We have investigated how to make the causal optimal filter by replacing the nonminimum phase components with the frequency components of the primary path. Through the computer simulations, we have confirmed that this filter maintained some noise reduction performance and can be used as a quasi-optimal filter. In this paper, as another approach, we attempt to identify noncausal components using the pre-trained adaptive noise control filter. The nonminimum phase components of the secondary path exist in the frequency band below the lowest resonance frequency of the secondary loudspeaker. Based on this fact, we design a noise control filter by using band-limited white noise only with the low frequency components below the lowest resonance frequency in advance. Then, we design another adaptive noise control filter by using the band-limited white noise with high frequency components above the lowest resonance frequency. Finally, we combine these filters in the frequency domain. Through the computer simulations, we show the difficulty to handle the nonminimum phase components in the ANC system.

Quantized information-theoretic learning based Laguerre functional linked neural networks for nonlinear active noise control

Traditional functional linked neural networks (FLNNs) impose a significant computational burden due to their input expansion, primarily stemming from the utilization of digital filters. This paper presents a Laguerre FLNNs filter for nonlinear active noise control (NANC) systems. By employing the truncated Laguerre series, the presented filter achieves effective approximation of long primary paths with a reduced filter length. Moreover, we develop adaptive algorithms rooted in information-theoretic learning (ITL) within the framework of the Laguerre-FLNNs NANC model. Using the ITL criterions, a Laguerre filtered-s maximum correntropy criterion (LFsMCC) algorithm is derived and a Laguerre filtered-s quantized minimum error entropy criterion (LFsQMEE) algorithm is proposed by minimizing Renyi’s quadratic entropy. To reduce the computation cost, an online vector quantization method is utilized to improve the LFsQMEE. This technique selectively quantizes the error vectors, reducing them to a smaller subset of samples within the codebook. Moreover, an enhanced LFsQMEE with a fiducial point is introduced. The steady-state performance and the computational complexity are analyzed. Theoretical analysis is validated through simulations and the control performance of the proposed model and algorithms is tested in experiments with both simulated and real paths.

Rational b-spline adaptive filter for active noise control of machinary noises

Spline adaptive filter has a different architecture than linear-in-parameter nonlinear filters like Volterra filter. There are various kinds of splines like Bezier spline, B-spline and rational B-spline. Rational B spline has weights associated with control points and hence, provides more flexibility than B-spline to create a curve. This paper presents development of rational b-spline adaptive filter for active noise control. Updating equations to update control points and weights of control points are derived. A simulation study is presented to study performance of proposed rational B-spline adaptive filter to reduce machinary noises. Performance of proposed rational B-spline filter are compared with B-spline filter and Bezier filter for active noise control of experimentally recorded noises of band-saw, CNC machine and compressor

Robust improved multiband-structured subband adaptive filter for active noise control with impulsive interference

The feedforward filtered-x least mean square algorithm is extensively implemented for active control of broadband noise. However, the control performance is substantially deteriorated due to colored noise and the presence of uncorrelated disturbances near the reference and error sensors. To tackle these issues, in this paper, a robust improved multiband-structured subband adaptive filter based on logarithmic and total least squares method is proposed for active control. Unlike the conventional method of total least squares, the proposed algorithm adopts logarithmic and Rayleigh quotient functions. The closed loop implementation of the improved multiband-structured subband adaptive filter is adopted to meet the delayless requirement. The proposed algorithm is well-suited for environments where the reference signal is highly correlated and the residual noise is contaminated by impulsive noise. Furthermore, an affine combination of the proposed algorithm is developed to meet the complementary requirements of faster convergence and improved noise reduction. Eventually, the stability and computational complexity are studied. Simulation results using measured acoustic paths in an anechoic chamber and a normal room illustrate the effectiveness of the proposed algorithm for controlling broadband noise with impulsive interference. In addition, the tracking control performance is evaluated in a time-varying acoustic environment.

Warmstarting strategies for convex optimization based multi-channel constrained active noise control filter design

In real-world applications of active noise control (ANC) systems, various constraints are supposed to be satisfied in the controller design process. The optimal control filter coefficients can be obtained by solving a constrained optimization problem, which usually requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC filter design. The proposed formulation was shown to result in a computational time reduction by several orders of magnitude. It is of great interest to further improve its efficiency by using a priori information of the optimal filter coefficients. One potential way of achieving this goal is to introduce a warmstart technique so that the filter solution of a similar system or environment can be referred to for selecting the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method, which, in general, is challenging for applying warmstart techniques. In the current work, relaxation methods are proposed to the constraints of original ANC filter design formulation so that the warmstart techniques can be applied. Then, a warmstarting technique proposed in previous study is used to solve a series of perturbed problems, and the performance of the warmstarting technique is investigated. Results show that with the proposed modifications applied, the warmstarting strategy can significantly reduce the number of iterations needed for solving the conic formulation of the ANC filter design problem without much tuning efforts, and the method is effective and robust in various environmental setups.

A Stable IIR Filter Design Approach for High-Order Active Noise Control Applications

In commercial non-adaptive active noise control (ANC) applications, an IIR filter structure is often used to reduce real-time computations. On the contrary, an FIR filter structure is usually preferred in the filter design phase because the FIR filter design formulation can be convex and is simple to solve. To combine the benefits of both FIR and IIR filter structures, one common approach in ANC applications is to use an IIR filter structure to fit a pre-designed FIR filter. However, to ensure stability, most of the common IIR filter fitting approaches involve the computation and relocation of poles which can be difficult for high-order cases. In this current work, a stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in ANC applications. The results demonstrate that the proposed method can achieve better fitting accuracy and steady-state noise control performance in high-order non-adaptive applications when the pre-designed noise control FIR filter is fitted. Besides fitting the noise control filter, the proposed method can also be used to fit the secondary path and acoustic feedback path to reduce the required real-time computations if adaptive controllers are applied.

An adaptive constrained multi-channel active noise control filter design approach using convex cone optimization

In current practical active noise control (ANC) applications, solutions to three main technical challenges need to be sought: the requirement of a stable controller when acoustic feedback paths exist, a larger quiet zone, and adaptation to a time-varying environment. The imposed controller stability constraints can significantly increase the computational requirements and negatively impact the adaptation of ANC filters in real time. Multi-channel systems are usually needed if a larger quiet zone is required while the coupling between different channels can greatly lower the convergence rate of adaptive algorithms. In the current work, a multi-channel adaptive constrained ANC filter design method is proposed. The recently proposed convex cone formulation for ANC design is adopted to reduce the computational time of solving the constrained ANC filter design problem. The optimal filter coefficients are then redesigned continuously using convex optimization when the environment is time-varying. The experimental result shows that, compared with the traditional leaky FxLMS method, the proposed method has a faster convergence rate and a better steady-state noise control performance.

Interpolated Individual Weighting Subband Volterra Filter for Nonlinear Active Noise Control

Nonlinear active noise control (NLANC) is always a challenge in algorithm design. Most of the NLANC algorithms are based on the linear-in-the-parameters (LIP) filters, and no work is conducted on subband adaptive filter (SAF). In this brief, a novel nonlinear SAF, termed the Volterra filtered-x normalized SAF (VFxNSAF), is proposed for NLANC, whose input vector is obtained according to the size of the analysis filter bank. Moreover, the virtual microphone strategy is applied to VFxNSAF to suppress the noise at a remote location. To mitigate the computational burden, the interpolated IWVFxNSAF with individual weighting (IW) (I-IWVFxNSAF) is proposed, in which the quadratic kernel is obtained by the interpolated filter. Simulation results corroborate the superiority of the VFxNSAF and I-IWVFxNSAF algorithms for NLANC.

A constrained adaptive active noise control filter design method via online convex optimization

In practical active noise control (ANC) applications, various types of constraints may need to be satisfied, e.g., robust stability, disturbance enhancement, and filter output power constraint. Some adaptive filters such as leaky LMS have been developed to apply required constraints indirectly. However, when multiple constraints are required simultaneously, satisfactory noise performance is difficult to achieve by tuning only one leaky factor. Another filter design approach that may achieve better noise control performance is to solve a constrained optimization problem. But the computational complexity of solving such a constrained optimization problem for ANC applications is usually too high even for offline design. Recently, a convex optimization reformulation is proposed which significantly reduces the required computational effort in solving constrained optimization problems for active noise control applications. In the current work, a constrained adaptive ANC filter design method is proposed. The previously proposed convex formulation is improved so that it can be implemented in real-time. The optimal filter coefficients are then redesigned continuously using online convex optimization when the environment is time-varying.

An active noise control filter design method based on machine learning algorithms

Filter design is the essential problem in active noise control. In the case of FIR filter design, the whole problem can be formulated as a convex optimization. In practice, limited by computation capability, IIR filters are preferred but more challenging to design. On the one hand, the existence of zeros could cause instablity; on the other hand, the problem can not be formulated as a convex optimization problem. This work introduces a new IIR filter design method, which stablizes the system by modeling the ANC controller as casade parametric biquadratic IIRs and optimizes their cofficients by using machine learning algorithms. A neural network with zero input but learnable bias and network weights is used to generate the filter coefficients; and the loss function consists of a reward term for reducing noise and penalty terms for breaking the constraints. Training the neural network with gradient based machine learning algorithm directly leads to a group of coefficients that achieves good ANC performance and is subject to given constraints. It turned out that no big and deep neurual network is required for this method to perform well and therefore it is computationally efficient. Experiments showed that the proposed method was able to consistently yield good ANC filters for a variety of given acoustical environments.

Low-complexity even mirror fourier adaptive filter for nonlinear active noise control

The Even Mirror Fourier (EMF) filter is the universal approximation for nonlinear systems, which has been used in active noise control (ANC) applications, especially in scenarios where ANC contains strong nonlinearity. However, the computational burden can impede its implementation in practice. To mitigate this disadvantage, an improved pipelined EMF (IPEMF) filter has been developed and applied for the nonlinear ANC systems, in this paper. The proposed architecture uses simple small-scale EMF modules (i.e., fewer coefficients) nested in a pipelined fashion to replace the complex EMF structure, and hence has got a computational advantage. Moreover, the modules of the IPEMF are designed to update the synaptic weight vector independently, and the output of IPEMF is simplified by the sum of the local estimates of the modules. As a consequence, the nonlinear processing capability is considerably improved and the filtered-error algorithm deduced for the IPEMF controller is less complicated. Simulation results show that the proposed IPEMF controller significantly reduces the computational complexity compared to EMF, while still maintaining control performance is as equivalent as EMF and better than the pipelined EMF (PEMF), pipelined Volterra filter (PVF).

Delayless polyphase implementation of filters in active noise control systems

In real-time implementation of active noise control filters, high sampling rate is sometimes preferred to reduce the delay in analog-to-digital converters or to reduce the risk of aliasing effect. A multi-rate structure is usually implemented with a polyphase structure to maintain a low sampling rate for the control filters to avoid the increase of real-time computational load. However, the use of decimation or interpolation filter will introduce additional delay, which can negatively affect the noise control performance. In the current work, a delayless implementation of polyphase structure is proposed where the original active noise control filter is first constrained to have sufficient attenuation at high frequencies in its design phase and is then decomposed into two multiplicative sub-filters, each of which involves a sufficiently high frequency attenuation. These two decomposed sub-filters can perform both noise control and decimation/interpolation without introducing additional delay in the polyphase structure. The proposed delayless approach can thus reduce the delay of a traditional multi-rate active noise control system and, in principle, can provide better active noise control performance. Moreover, if a single rate system is implemented at a high sampling rate, the proposed polyphase structure in filter implementation can effectively reduce the real-time computational load.

Implementation of robust virtual sensing algorithm in active noise control to improve silence zone

Active noise control (ANC) is a successful technique to reduce unwanted noise based on the superposition principle. In a conventional ANC system, the extent of unwanted noise can be attenuated at the error microphone location, thus making a silent zone at the desired location. However, in certain situations, it is impossible to place the error microphone at the desired location. In that case, the error microphone cannot assure adequate noise suppression at the desired location. To overcome that, the virtual sensing technique (VST) has been implemented in ANC to shift the zone of silence to the desired position. This paper proposes a supplemental filter in VST to avoid interference issues between secondary and virtual paths..In the virtual ANC, the supplemental filter H provides the required information to measure optimal noise control filter and also increases noise reduction in the ANC system at the virtual location. A Real-Time Simulink model is designed for the proposed virtual sensing ANC and evaluate its efficiency. The computer simulation findings showed that the ANC system performance with the proposed virtual sensing method had good noise reduction at the virtual location compared to the physical location. The proposed supplemental filter preserves reasonable noise reduction efficiency in the ANC system if the physical microphone is positioned far from the location of the silence zone.

A generalized collaborative functional link adaptive filter for nonlinear active noise control

This paper derives a collaborative control algorithm called generalized collaborative functional link adaptive filter (GCFLAF) for nonlinear active noise control (NANC). The algorithm adopts the collaborative scheme by handling the noise cancellation problem divisionally and parallelly, and working coordinately. It takes the characteristics of different nonlinear components into consideration and handles them separately. And a hierarchical adaption law is adopted in which linear filter is always prior to nonlinear filters no matter whether nonlinear distortions arise from the primary path as required by the filtering scenario. Thus the proposed scheme can tailor to different nonlinear characters arising from the primary path and can hierarchically adapt to the influences of the distinct nonlinearities. Particularly, since the zero-memory nonlinearity and memory nonlinearity are often unavoidable in NANC, it employs two shrinkage parameters to regulate the contribution of the different degrees of memory and zero-memory nonlinearity as required by the filtering scenario, aiming to achieve a better convergence performance and robustness to nonlinear distortions. Some numerical simulation results in the context of random noises as well as the real noise signals verify the improved convergence behavior of the presented architecture in NANC scenarios.

Multirate Audio-Integrated Feedback Active Noise Control Systems Using Decimated-Band Adaptive Filters for Reducing Narrowband Noises.

Audio-integrated feedback active noise control (AFANC) systems deliver wideband audio signals and cancel low frequency narrowband noises simultaneously. The conventional AFANC system uses single-rate processing with fullband adaptive active noise control (ANC) filter for generating anti-noise signal and fullband audio cancelation filter for audio-interference cancelation. The conventional system requires a high sampling rate for audio processing. Thus, the fullband adaptive filters require long filter lengths, resulting in high computational complexity and impracticality in real-time system. This paper proposes a multirate AFANC system using decimated-band adaptive filters (DAFs) to decrease the required filter lengths. The decimated-band adaptive ANC filter is updated by the proposed decimated filtered-X least mean square (FXLMS) algorithm, and the decimated-band audio cancelation filter can be obtained by the proposed on-line and off-line decimated secondary-path modeling algorithms. The computational complexity can be decreased significantly in the proposed AFANC system with good enough noise reduction and fast convergence speed, which were verified in the analysis and computer simulations. The proposed AFANC system was implemented for an active headrest system, and the real-time performances were tested in real-time experiments.

BIBO-stable implementation of adaptive function expansion bilinear filter for nonlinear active noise control

The preeminent merit of function expansion bilinear (FEB) filters is their ability to represent nonlinear distributions for active noise control (ANC) systems. Unfortunately, the huge computational burden and bounded input bounded output (BIBO) unstable problem hinder its practical applications. In this paper, we propose a general channel reduced efficient implementation algorithm for FEB filter and two BIBO stable control methods, to further reduce the computational load and overcome the unstable problem. The efficiency of the proposed methods is verified by computational complexity analyses and computer simulations for nonlinear ANC (NANC) systems. The results of computational analysis and computer simulation show the satisfied control performances with significant computational reduction.

Hierarchical partial update generalized functional link artificial neural network filter for nonlinear active noise control

To reduce the computational burden of the generalized FLANN (GFLANN) filter for nonlinear active noise control (NANC), a hierarchical partial update GFLANN (HPU-GFLANN) filter is presented in this paper. Based on the principle of divide and conquer, the proposed HPU-GFLANN divides the complex GFLANN filter (i.e., long memory length and large cross-terms selection parameter) into simple small-scale GFLANN modules and then interconnected in a pipelined form. Since those modules are simultaneously performed in a parallelism fashion, there is a significant improvement in computational efficiency. Besides, a hierarchical learning strategy is used to avoid the coupling effect between the nonlinear and linear part of the pipelined architecture. Data-dependent hierarchical M-Max filtered-error LMS algorithm is derived to selectively update coefficients of the HPU-GFLANN filter, which can further reduce the computational complexity. Moreover, the convergence analysis of the NANC system indicates that the proposed algorithm is stable. Computer simulation results verify that the proposed adaptive HPU-GFLANN filter is more effective in nonlinear ANC systems than the FLANN and GFLANN filters.

M-max partial update leaky bilinear filter-error least mean square algorithm for nonlinear active noise control

To reduce the computational burden of the bilinear FLANN (BFLANN) filter for active noise control (ANC), an M-max partial update leaky bilinear filtered-error least mean square (MmLBFE-LMS) algorithm is proposed in this paper. Unlike the algorithm based on filtered-reference technique in BFLANN-based ANC system, the proposed MmLBFE-LMS algorithm uses the filtered-error method and data-dependence partial update strategy to reduce computational complexity, and employs a leaky technique to mitigate the instability problem as in bilinear filters. The simulation results and computational complexity analysis indicate that the proposed algorithm can significantly reduce the computational burden of the BFLANN-based ANC system without suffering from noise-canceling performance degradation.

Variable Threshold-Based Selective Updating Algorithms in Feed-Forward Active Noise Control Systems

Selective updating (SU)-based adaptive algorithms are proposed for secondary path estimation and noise control in active noise control systems. Use of the proposed variable threshold (VT) for noise control filter aids in reducing the computational complexity of filtered-x LMS-Newton algorithm to achieve fast convergence and improved noise reduction irrespective of the eigen-spread of input signal correlation matrix. A VT-SU least mean square algorithm is presented for the online estimation of the secondary path that reduces computational cost while maintaining estimation accuracy and convergence speed. A power scheduling scheme is presented that requires only one tunable parameter and discontinues auxiliary noise for power level below a predefined limit to reduce the residual error signal. The proposed VT-SU algorithms allow frequent updates in the transition phase and fewer updates in the steady state. Simulations are performed under benchmark conditions to validate the improved performance of the proposed method in comparison with established state-of-the-art methods in terms of estimation accuracy, steady-state residual error, convergence speed, number of tunable parameters, tracking capability, and computational complexity.

Improved adaptive recursive even mirror Fourier nonlinear filter for nonlinear active noise control

In this paper, we analyze the theoretical mechanism for the effectiveness of recursive filters including both linear and nonlinear feedforward and feedback subsections to accurately approximate nonlinear distributions in the active noise control (ANC) system. As a result, we improve the recursive even mirror Fourier nonlinear (REMFN) filter by adding an additional linear section termed REMFNL filter together with its channel reduced form (CRREMFNL) to explore better control performance. As for the linear feedback section introduced, we have studied the bound-input bound-output (BIBO) stability condition for the REMFNL filter and designed a stable control scheme to guarantee the filter satisfying the stability criteria. The performance of the proposed filters equipped with a filtered-x least mean square (FXLMS) algorithm is validated through analyses of computational complexity and simulations of various nonlinearities for nonlinear ANC (NANC) systems. Simulation results demonstrate that the proposed REMFNL and CRREMFNL filters can achieve better performance over the bilinear, recursive second-order Volterra (RSOV), recursive functional link artificial neural network (RFLANN) and standard REMFN filters based on the FXLMS algorithm, which often outperform the conventional Volterra FXLMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms.