The affine projection (AP) algorithm enhances the performance of gradient-based adaptive algorithms when dealing with colored reference signals, which is typically the case with filtered-X type algorithms. This enhancement is achieved by using various delayed versions of the reference signal data vector, which are appropriately orthogonalized and normalized to optimize convergence performance. The number of these vectors, known as the projection order of the AP, increases the computational requirements, mainly due to the calculation of a matrix inversion whose dimensions are proportional to this projection order. When used in distributed systems, the AP algorithm typically requires each acoustic node in the system to compute the complete matrix inversion, even though they only need a specific set of data (a subblock) from it. This means that the AP does not offer much advantage in terms of computational savings when used in distributed collaborative networks. To address this issue, an approximate version of the filtered-X affine projection (FXAP) algorithm is introduced in this work. This approximate version avoids the matrix inversion computation in each iteration using a precalculated inverse matrix. This strategy provides computational savings and enables easy distribution of the algorithm. Additionally, a variable step-size approach is proposed to mitigate the deviation caused by a precalculated matrix, which provides good performance, high robustness, and cost-effective distribution.

This paper addresses the assessment of the stability of distributed active noise control (ANC) systems, which are designed to cancel acoustic noise at given points in space. These systems distribute the control task across several simple acoustic nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated by the filtered-X LMS algorithm. The nodes remain stable when the adaptive filters computed in each node converge to finite values. However, the acoustic coupling among nodes can cause instability (i.e., divergence). Collaboration among nodes is required to avoid this phenomenon. It is shown that the properties of the system are summarized in a system matrix and that the system remains stable when the real parts of all of the eigenvalues of this system matrix are positive. However, computation of all of the eigenvalues is computationally expensive. In this paper, we propose a fast method for checking the positiveness of the real parts of the system matrix eigenvalues. It is shown that the proposed method is faster than the direct calculation of eigenvalues and it assesses the stability/instability of the ANC systems without any false stability outcomes and more accurately than existing alternatives.

The choice of a suitable convergence step that allows the fast convergence of the filtered-x LMS algorithm in practical scenarios is usually carried out by trial and error, since the theoretical developments provide only indicative values. The particularity of the filtered-x structure, which adds a delay between the output of the adaptive filter and the error signal and colors the reference signal, increases the inaccuracy of the theoretical models. Furthermore, the use of band-limited reference signals is beyond the scope of most theoretical studies, which focus on the cases of full-band reference signals, making it difficult to extrapolate these models to band-limited signals. In this paper, we propose a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases. It can be used regardless of the type of the reference signal, the system delays, and the nature of the filter required in the filtered-x structure. Numerical simulations are performed to validate the effectiveness of the proposed approach.

Multichannel Active Noise Control (ANC) headrest systems have usually been designed with the objective of creating quiet areas at the passenger positions within the cabin of a public transport. Due to the high computational demands of dealing with multiple loudspeakers and multiple microphones by using a single centralized processor, and the convenience of a scalable system, a distributed implementation may be advisable. On the other hand, the addition of the remote microphone (RM) technique to the ANC headrest systems has recently allowed the creation of local zones of quiet at unachievable placements for the error sensors. This technique allows the quiet zone to be shifted to a desired location away from the physical sensor. However, to our knowledge, the implementation of an ANC headrest system with virtual microphones over a distributed acoustic sensor network has not been addressed. In this work, a distributed version of the multiple-error FxLMS (MEFxLMS) algorithm considering the RM method (RM-DMEFxLMS) is proposed by using an alternative formulation of the RM method. Through a set of simulations, it is found that on a non-constrained communication network, the proposed algorithm presents the same performance of its centralized version and provides a scalable and more versatile ANC system.

In this work we propose a multi-channel active noise equalizer (ANE) that can deal with multi-frequency noise signals and assigns simultaneously different equalization gains to each frequency component at each monitoring sensor. For this purpose, we state a pseudo-error noise signal for each sensor of the ANE, which has to be cancelled out in order to get the desired equalization profiles. Firstly the optimal analytic solution for the ANE filters in the case of single-frequency noise is provided, and an adaptive algorithm based on the Least Mean Squared (LMS) is proposed for the same case. We also show that this adaptive strategy reaches the theoretical solution in steady state. Secondly, we state an equivalent approach for the case of multi-frequency noise based on two alternatives: a common pseudo-error signal at each sensor for all frequencies, and a different pseudo-error signal at each sensor for each frequency. The analytic and adaptive solutions for the ANE control filters have been developed for both pseudo-error alternatives. Finally, the ability of the proposed ANE to achieve simultaneously different user-selected noise profiles in different locations has been validated by their transfer functions and simulations.

Acoustic sensor networks (ASNs) are an effective solution to implement active noise control (ANC) systems by using distributed adaptive algorithms. On one hand, ASNs provide scalable systems where the signal processing load is distributed among the network nodes. On the other hand, their noise reduction performance is comparable to that of their respective centralized processing systems. In this sense, the distributed multiple error filtered-x least mean squares (DMEFxLMS) adaptive algorithm has shown to obtain the same performance than its centralized counterpart as long as there are no communications constraints in the underlying ASN. Regarding affine projection (AP) adaptive algorithms, some distributed approaches that are approximated versions of the multichannel filtered-x affine projection (MFxAP) algorithm have been previously proposed. These AP algorithms can efficiently share the processing load among the nodes, but at the expense of worsening their convergence properties. In this paper we develop the exact distributed multichannel filtered-x AP (EFxAP) algorithm, which obtains the same solution as that of the MFxAP algorithm as long as there are no communications constraints in the underlying ASN. In the EFxAP algorithm each node can compute a part or the entire inverse matrix needed by the centralized MFxAP algorithm. Thus, we propose three different strategies that obtain significant computational saving: 1) Gauss Elimination, 2) block LU factorization, and 3) matrix inversion lemma. As a result, each node computes only between 25% - 60% of the number of multiplications required by the direct inversion of the matrix. Regarding the performance in transient and steady states, the EFxAP exhibits the fastest convergence and the highest noise level reduction for any size of the acoustic network and any projection order of the AP algorithm compared to the DMEFxLMS and two previously reported distributed AP algorithms.

This paper focus on the implementation of an active noise control system over a network of distributed nodes acoustically coupled. We have considered the distributed Multiple Error filtered-x Least Mean Square (DMEFxLMS) algorithm that allows collaboration between nodes following an incremental strategy. To reduce the computational network requirements, an alternative strategy which brings together only the acoustically coupled nodes has been used. However, a rule to define the subsets of nodes that are required to collaborate is needed. A collaborative condition based on the analysis in the frequency domain of the eigenvalues of the acoustic path matrix is proposed. Results demonstrate the ability of the introduced method to define the subsets of nodes that collaborate.

Wave field synthesis (WFS) is a multichannel audio reproduction method, of a considerable computational cost that renders an accurate spatial sound field using a large number of loudspeakers to emulate virtual sound sources. The moving of sound source locations can be improved by using fractional delay filters, and room reflections can be compensated by using an inverse filter bank that corrects the room effects at selected points within the listening area. However, both the fractional delay filters and the room compensation filters further increase the computational requirements of the WFS system. This paper analyzes the performance of a WFS system composed of 96 loudspeakers which integrates both strategies. In order to deal with the large computational complexity, we explore the use of a graphics processing unit (GPU) as a massive signal co-processor to increase the capabilities of the WFS system. The performance of the method as well as the benefits of the GPU acceleration are demonstrated by considering different sizes of room compensation filters and fractional delay filters of order 9. The results show that a 96-speaker WFS system that is efficiently implemented on a state-of-art GPU can synthesize the movements of 94 sound sources in real time and, at the same time, can manage 9216 room compensation filters having more than 4000 coefficients each.

This paper considers the effect of effort constraints on the behavior of an active noise control (ANC) system over a distributed network composed of acoustic nodes. A distributed implementation can be desirable in order to provide more flexible, versatile, and scalable ANC systems. In this regard, the distributed version of the multiple error filtered-x least mean square (DMEFxLMS) algorithm that allows collaboration between nodes has shown excellent properties. However, practical constraints need to be considered since, in real scenarios, the acoustic nodes are equipped with power constrained actuators. If these constraints are not considered within the adaptive algorithm, the control signals may increase and saturate the hardware devices, causing system instability. To avoid this drawback, a control effort weighting can be considered in the cost function of the distributed algorithm at each node. Therefore, a control effort strategy over the output signals at each node is used to keep them under a given threshold and ensuring the distributed ANC system stability. Experimental results show that, assuming ideal network communications, the proposed distributed algorithm achieves the same performance as the leaky centralized ANC system. A performance evaluation of several versions of the leaky DMEFxLMS algorithm in realistic scenarios is also included.

Room equalization has become essential for sound reproduction systems to provide the listener with the desired acoustical sensation. Recently, adaptive filters have been proposed as an effective tool in the core of these systems. In this context, this paper introduces different novel schemes based on the combination of adaptive filters idea: a versatile and flexible approach that permits obtaining adaptive schemes combining the capabilities of several independent adaptive filters. In this way, we have investigated the advantages of a scheme called combination of block-based adaptive filters which allows a blockwise combination splitting the adaptive filters into nonoverlapping blocks. This idea was previously applied to the plant identification problem, but has to be properly modified to obtain a suitable behavior in the equalization application. Moreover, we propose a scheme with the aim of further improving the equalization performance using the a priori knowledge of the energy distribution of the optimal inverse filter, where the block filters are chosen to fit with the coefficients energy distribution. Furthermore, the biased block-based filter is also introduced as a particular case of the combination scheme, especially suited for low signal-to-noise ratios (SNRs) or sparse scenarios. Although the combined schemes can be employed with any kind of adaptive filter, we employ the filtered-x improved proportionate normalized least mean square algorithm as basis of the proposed algorithms, allowing to introduce a novel combination scheme based on partitioned block schemes where different blocks of the adaptive filter use different parameter settings. Several experiments are included to evaluate the proposed algorithms in terms of convergence speed and steady-state behavior for different degrees of sparseness and SNRs.

This paper provides an analysis of the steady-state behavior of two biased adaptive algorithms recently introduced for listening room compensation, the biased filtered-x normalized least mean squares (Fx-BNLMS) and the biased filtered-x improved proportionate NLMS (Fx-BIPNLMS). We give theoretical results that show that the biased algorithms can outperform the unbiased ones in terms of the mean square error, especially in low signal-to-noise ratio (SNR) scenarios. Moreover, for impulse responses exhibiting high sparse-ness, the improved proportionate algorithms achieve faster convergence than the standard NLMS. Thereby, the advantages of the Fx-BIPNLMS algorithm are justified theoretically in terms of the excess mean square error. Simulation results show that there is a relatively good match between theory and practice, especially for low μ values.

Multichannel adaptive equalization (AE) systems require high computational capacity, which constraints their practical implementation. Graphics Processing Units (GPUs) are well known due to their potential for highly parallel data processing. Although the GPUs seem to be suitable platforms for multichannel scenarios, an efficient use of parallel computation in the adaptive filtering context is not straightforward due to the feedback loops. This paper presents a GPU implementation of a multichannel AE system based on the filtered-x LMS algorithm working over a real-time prototype. Details of the parallelization of the algorithm are given. Experimental results are presented to validate and computationally analyze the real-time performance of the AE GPU implementation. Results show the usefulness of GPUs to develop versatile, scalable and low cost multichannel AE systems.

Multichannel active noise control (ANC) systems are commonly based on adaptive signal processing algorithms that require high computational capacity, which constrains their practical implementation. Graphics Processing Units (GPUs) are well known for their potential for highly parallel data processing. Therefore, GPUs seem to be a suitable platform for multichannel scenarios. However, efficient use of parallel computation in the adaptive filtering context is not straightforward due to the feedback loops. This paper compares two GPU implementations of a multichannel feedforward local ANC system working as a real-time prototype. Both GPU implementations are based on the filtered-x Least Mean Square algorithms; one is based on the conventional filtered-x scheme and the other is based on the modified filtered-x scheme. Details regarding the parallelization of the algorithms are given. Finally, experimental results are presented to compare the performance of both multichannel ANC GPU implementations. The results show the usefulness of many-core devices for developing versatile, scalable, and low-cost multichannel ANC systems.

This study is focused on the necessity to improve the performance of the affine projection (AP) algorithm for active noise control (ANC) applications. The proposed algorithms are evaluated regarding their steady‐state behaviour, their convergence speed and their computational complexity. To this end, different strategies recently applied to the AP for channel identification are proposed for multichannel ANC. These strategies are based either on a variable step size, an evolving projection order, or the combination of both strategies. The developed efficient versions of the AP algorithm use the modified filtered‐x structure, which exhibits faster convergence than other filtering schemes. Simulation results show that the proposed approaches exhibit better performance than the conventional AP algorithm and represent a meaningful choice for practical multichannel ANC applications.

Adaptive filtering schemes exhibit a compromise between convergence speed and steady-state mean square error. Trying to overcome this trade-off, convex combination of adaptive filters have been recently developed for system identification achieving better performance than traditional approaches. The purpose of this work is to apply the convex combination strategy to single-channel and multichannel active noise control systems. In these systems it is necessary to take into account the secondary path between the adaptive filter output and the error sensor and the possible unavailability of the disturbance signal, which depends on the filtering scheme considered. Even though this strategy involves a higher computational burden than the classic adaptive filters, it exhibits a good performance in terms of convergence speed and steady-state mean square error.

Affine projection (AP) algorithms have been proposed in recent years for use in active noise control systems. This is due to their potential high convergence speed along with their robustness and moderate computational cost. However, these algorithms can exhibit an excessive computational cost for high projection orders (just when higher convergence speed is achieved). Thus, computationally efficient versions of these algorithms have been proposed. For the particular case of the AP algorithms applied to active noise control, the use of the conventional filtered-x structure instead of the commonly used modified filtered-x method can be understood as an efficient strategy, since it needs fewer operations to update the adaptive filter coefficients. However, the use of this structure implies different algorithm behavior for the following two reasons: the signals needed in the coefficient updates do not correspond exactly to the AP algorithm and this structure introduces a delay between the update of the adaptive filter coefficients and its effect on the noise signal. In practice, this dual effect mainly affects convergence of the algorithms in the transient regime. This correspondence presents a mathematical model so that the transient behavior of the conventional filtered-x AP algorithm can be predicted from the reference signal statistics and algorithm parameters.

This paper provides an analysis of the steady-state behavior of the filtered-x affine projection algorithm (FXAP). This efficient affine projection (AP) algorithm for active noise control (ANC) applications is based on the filtered-x scheme, unlike most AP algorithms based on the more computationally demanding modified filtered-x scheme. This study depends on energy conservation arguments and does not require an specific signal distribution. The theoretical expressions derived for the mean square error (MSE) allowed to accurately predict the steady-state performance of the FXAP for meaningful practical cases. Simulation results of a single-channel ANC system validate the analysis and the theoretical expressions derived.

In recent years, affine projection algorithms have been proposed for adaptive system applications as an efficient alternative to the slow convergence speed of least mean square (LMS)-type algorithms. Whereas much attention has been focused on the development of efficient versions of affine projection algorithms for echo cancellation applications, the similar adaptive problem presented by active noise control (ANC) systems has not been studied so deeply. This paper is focused on the necessity to reduce even more the computational complexity of affine projection algorithms for real-time ANC applications. We present some alternative efficient versions of existing affine projection algorithms that do not significantly degrade performance in practice. Furthermore, while in the ANC context the commonly used affine projection algorithm is based on the modified filtered-x structure, an efficient affine projection algorithm based on the (nonmodified) conventional filtered-x structure, as well as efficient methods to reduce its computational burden, are discussed throughout this paper. Although the modified filtered-x scheme exhibits better convergence speed than the conventional filtered-x structure and allows recovery of all the signals needed in the affine projection algorithm for ANC, the conventional filtered-x scheme provides a significant computational saving, avoiding the additional filtering needed by the modified filtered-x structure. In this paper, it is shown that the proposed efficient versions of affine projection algorithms based on the conventional filtered-x structure show good performance, comparable to the performance exhibited by the efficient approaches of modified filtered-x affine projection algorithms, and also achieve meaningful computational savings. Experimental results are presented to validate the use of the algorithms introduced in the paper for practical applications.

An efficient version of the affine projection (AP) algorithm, which is called FXAP-AC throughout the paper, is presented. This algorithm uses the filtered-x structure instead of the modified structure which is required for the implementation of the AP algorithm when the desired signal is not available, for instance in active noise control (ANC) applications. The conventional AP algorithm for ANC, which is based on the modified structure (MFXAP), provides good performance. However the filtered-x structure is advisable for practical cases since it achieves a meaningful computational saving avoiding the additional filtering needed by the modified structure without significantly affect the performance in practice. In this paper, an efficient computation of coefficient update is developed for the FXAP resulting in the FXAP-AC. This low-cost strategy already proposed in the conventional AP algorithm can be suitably combined with others previously reported to achieve very fast and robust FXAP algorithms. Experimental results validate the use of the proposed algorithm for practical applications

An algorithmic variant of the conventional active noise equalizer (ANE), which independently controls some given frequencies of the primary signal, has been developed and extended to the multichannel case. The modified version of the ANE is named common-error multiple-frequency ANE. A detailed analysis of both multichannel equalizers has been carried out. From a convergence analysis in the frequency-domain, the significance of transducer locations in the behavior of a practical system can be predicted through the matrix of secondary path responses at each frequency. The ANEs steady-state transfer functions from the primary input signal to the noise output have also been developed and compared for different parameter settings and for accurate and inaccurate secondary path estimation. Furthermore, the multichannel extension of both equalizers has been implemented in a real-time active system inside a listening room for multifrequency noise. Useful-size zones of equalization have been binaurally measured by using a head and torso simulator. It was found that the common-error multiple-frequency ANE performs better than the conventional equalizer because it achieves a saving in computational complexity and has smaller overshoot. It can also be implemented in a real controller more easily than the conventional ANE and without showing meaningful differences in the practical results provided.

Multichannel adaptive affine projection algorithms (multichannel AP) are currently under development for multichannel audio applications, mainly for transaural audio reproduction. These algorithms present several advantages for real time systems such as moderate computational cost, good stability, and adjustable convergence speed. However the basic version of the AP algorithm needs to be optimized to be used on digital signal processors working on real time. Thus several variants of AP and its fast version (FAP) have been developed. Regarding its computational cost and real time implementation, an N /spl times/ N inverse matrix have to be calculated in each algorithm iteration, being N the affine projection order. This paper presents a comparison between several versions of the AP algorithm for real time multichannel audio and proposes a series of recommendations, such as the initialization parameters, to use the variants of the AP algorithm in multichannel sound.

This work is a preliminary study which focuses on subjective improvements of vehicle interior noise by using active noise control techniques. A local active noise control system has been mounted inside a room in order to reduce synthesized and real engine noise in the area around the headrest of a typical car seat. Recordings before and after cancellation have been made using a head acoustics mannequin positioned in the seat with two calibrated microphones at the ear-canals. Two methods were used to evaluate the comfort improvements achieved by active noise control. First, a prediction model of comfort based on four psychoacoustic descriptors (loudness, roughness, sharpness and tonality) was applied. Secondly, the subjective evaluation of controlled signals was carried out by means of a jury test. The reduction of noise levels does not necessarily reduce the annoyance of car engine noise that depends on spectral characteristics of noise.

In this paper, a novel adaptive algorithm for equalization of periodic signals using active control is developed. This algorithm actively cancels out a single frequency without changing the amplitude levels at close frequencies. The algorithm performance is compared with that of an adaptive equalizer previously reported (Kuo and Ji 1995 and Kuo and Morgan 1996). Both algorithms are used for a real multichannel system in order to equalize some given frequencies of a primary signal. The local active noise control system has been used to create an equalization zone. A two channel system is used and the total pressure is controlled at two microphones. A 4100 type Bruel manikin with two calibrated microphones at the ear canals has been used to obtain sound levels in a hypothetic listener's ears. The equalization points are not only the error sensors positions but an area around them which is measured using the manikin.