Fast Transversal Filter Algorithm Research Articles

Partial Update Simplified Fast Transversal Filter Algorithms for Acoustic Echo Cancellation

Robust algorithms applied in Acoustic Echo Cancellation systems present an excessive calculation load that has to be minimized. In the present paper, we propose two different low complexity fast least squares algorithms, called Partial Update Simplified Fast Transversal Filter (PU-SMFTF) algorithm and Reduced Partial Update Simplified Fast Transversal Filter (RPU-SMFTF) algorithm. The first algorithm reduces the computational complexity in both filtering and prediction parts using the M-Max method for coefficients selection. Moreover, the second algorithm applies the partial update technique on the filtering part, joined to the P-size forward predictor, to get more complexity reduction. The obtained results show a computational complexity reduction from (7L+8) to (L+6M+8) and from (7L+8) to (L+M+4P+17) for the PU-SMFTF algorithm and RPU-SMFTF algorithm, respectively compared to the original Simplified Fast Transversal Filter (SMFTF). Furthermore, experiments picked out in the context of acoustic echo cancellation, have demonstrated that the proposed algorithms provide better convergence speed, good tracking capability and steady-state performances than the NLMS and SMFTF algorithms.

A new simplified fast transversal filter algorithm based on subband approach (SSFTF) for acoustic echo cancellation

This paper addresses the problem of acoustic echo cancellation (AEC) by adaptive filtering algorithms with low complexity. In this paper, we propose a subband implementation of the simplified fast transversal filter (SFTF) algorithm. The proposed subband SFTF (SSFTF) is derived for acoustic echo cancellation (AEC) application. The efficient proposed subband decomposition leads to an improvement of the convergence speed performance even in situation when very non-stationary signal is present at the input. The proposed SSFTF algorithm has shown robustness in the background noise presence case. The complexity and comparison of the proposed SSFTF algorithm with state of the art algorithms have shown its superiority in terms of convergence speed performance that is evaluated by the mean square error (MSE) and system mismatch (SM) objective criteria. Intensive experiments have been conducted on the new algorithm to show all the performance with different scenarios in AEC application. All the obtained results have shown the best performances and efficiency of the new SSFTF algorithm.

A fast convergence normalized least‐mean‐square type algorithm for adaptive filtering

SUMMARYA new adaptive algorithm with fast convergence and low complexity is presented. By using the calculation structure of the dual Kalman variables of the fast transversal filter algorithm and a simple decorrelating technique for the input signal, we obtain an algorithm that exhibits faster convergence speed and enhanced tracking ability compared with the normalized least‐mean‐square algorithm with similar computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.

Predictive FTF Adaptive Algorithm for Mobile Channels Estimation

The aim of this research paper is to improve the performance of Fast Transversal Filter (FTF) adaptive algorithm used for mobile channel estimation. A multi-ray Jakes mobile channel model with a Doppler frequency shift is used in the simulation. The channel estimator obtains the sampled channel impulse response (SIR) from the predetermined training sequence. The FTF is a computationally efficient implementation of the recursive least squares (RLS) algorithm of the conventional Kalman filter. A stabilization FTF is used to overcome the problem caused by the accumulation of roundoff errors, and, in addition, degree-one prediction is incorporated into the algorithm (Predictive FTF) to improve the estimation performance and to track changes of the mobile channel. The efficiency of the algorithm is confirmed by simulation results for slow and fast varying mobile channel. The results show about 5 to 15 dB improvement in the Mean Square Error (Deviation) between the estimated taps and the actual ones depending on the speed of channel time variations. Slow and fast vehicular channels with Doppler frequencies 100 Hz and 222 Hz respectively are used in these tests. The predictive FTF (PFTF) algorithm give a better channel SIR estimation performance than the conventional FTF algorithm, and it involves only a small increase in complexity.

A new fast Newton‐type adaptive filtering algorithm for stereophonic acoustic echo cancellation (SAEC)

AbstractThis paper addresses the problem of acoustic echo cancellation. We propose a new version of the fast Newton transversal filter algorithm for stereophonic acoustic echo cancellation applications. This algorithm can be viewed as an efficient implementation of the extended two‐channel fast transversal filter algorithm. Moreover, it fits naturally within the frame of the fast version of the recursive least‐squares (RLS) algorithm, applied to the two‐channel case. To stabilize the proposed two‐channel algorithm, we have adapted and then applied a new numerical stabilization technique that has been proposed recently. The computational complexity of the proposed two‐channel algorithm is less than half the complexity of the fastest two‐channel RLS versions and very close to that of the two‐channel normalized least mean squares algorithm when its predicting part length is chosen to be small. Simulation results and comparisons in term of complexities, convergence speed and tracking with the two‐channel algorithms are presented. Copyright © 2009 John Wiley & Sons, Ltd.

Active Noise Control for 3-Dimensional Sound Field Using Fast Converging Algorithms

Active control in 3 dimensional sound field against incoming noise from external noise source is considered. Convergence characteristics are investigated with not only conventionally wide-used Filtered-x LMS algorithm, but also FTF (fast transversal filter) and FDA (frequency domain adaptive) algorithms. The advantages and disadvantages of each technique are examined through simulations and experiments using 1/5 scale model. Control results are studied also with both fixed noise source and moving noise source, and the difference in the control performance of each algorithm is compared and considered. As a result of simulations and experiments, it is shown that the control performance of FTF and FDA are better than it of LMS for the fixed noise source. For the moving noise source, each performance of control becomes worse ; however, it is shown that control can be continued comparatively stably.

Practical implementation of multichannel adaptive filters based on FTF and AP algorithms for active control

AbstractIn this paper, multichannel affine projection (AP) algorithms and fast transversal filters (FTF) are introduced for active noise control. A comparative practical study of the mentioned algorithms with the filtered‐X LMS (F‐XLMS) and the recursive least squares (RLS) is presented for multichannel systems. This study is based on simulations using real data and is mainly focused on: their computational cost and memory load, their convergence properties, their stability and their ability to create quiet zones around listener ears. Simulations show that algorithms based on FTF exhibit a good trade‐off between computational cost and convergence speed. On the other hand, those based on RLS are slightly faster but they present higher computational load and stability problems in their practical implementation. It has also been observed that algorithms based on low order AP algorithms present less computational cost than the FTF‐based ones but a slightly slower convergence speed. Therefore these algorithms show a desirable behaviour and versatility for practical applications. Finally, results obtained in a real‐time multichannel system validate the use of AP algorithms in practical applications as an alternative to the classical multichannel F‐XLMS since they provide meaningful attenuation levels, lower convergence time and similar computational cost. Additionally, as simulations indicated, AP algorithm performance can be easily improved increasing its projection order and using fast versions. Copyright © 2004 John Wiley & Sons, Ltd.

408 高速に収束するアルゴリズムを用いた3次元の能動的音響制御

Active control in 3-dimensional sound field against incoming noise from external noise source is considered. Convergence characteristics are investigated with not only conventionally wide-used Filtered-x LMS algorithm, but also FTF (fast transversal filter) and FDA (frequency domain adaptive) algorithms. The advantages and disadvantages of each technique are examined through simulations and experiments using 1/5 scale model. Control results are studied also with both fixed noise source and moving noise source, and the difference in the control performance of each algorithm is compared and considered. As a result of simulations and experiments, it is shown that the control performance of FTF and FDA are better than it of LMS for the fixed noise source. For the moving noise source, each performance of control becomes worse; however, it is shown that control can be continued comparatively stably.

Fast subsampled-updating stabilized fast transversal filter (FSU SFTF) RLS algorithm for adaptive filtering

We present a new, doubly fast algorithm for recursive least-squares (RLS) adaptive filtering that uses displacement structure and subsampled-updating. The fast subsampled-updating stabilized fast transversal filter (FSU SFTF) algorithm is mathematically equivalent to the classical fast transversal filter (FTF) algorithm. The FTF algorithm exploits the shift invariance that is present in the RLS adaptation of an FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson (1947) algorithm. In the subsampled-updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur-type algorithm that, once properly initialized, does not require inner products. The various convolutions that appear In the algorithm are done using the fast Fourier transform (FFT). The resulting algorithm is doubly fast since it exploits FTF and FFTs. The roundoff error propagation in the FSU SFTF algorithm is identical to that in the SFTF algorithm: a numerically stabilized version of the classical FTF algorithm. The roundoff error generation, on the other hand, seems somewhat smaller. For relatively long filters, the computational complexity of the new algorithm is smaller than that of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation.

Multichannel RLS algorithms and FTF algorithms for active noise control and sound reproduction systems

In the fields of active noise control (ANC) and transaural sound reproduction (TSR), multichannel FIR adaptive filters are extensively used. For the learning of such FIR adaptive filters, recursive-least-squares (RLS) algorithms are known to typically produce a faster convergence speed than stochastic gradient descent techniques, such as the basic least-mean-squares (LMS) algorithm or even the fast convergence Newton-LMS, gradient-adaptive-lattice (GAL) LMS and discrete-cosine-transform (DCT) LMS algorithms. In this presentation, multichannel RLS algorithms and multichannel fast-transversal-filter (FTF) algorithms are introduced, with the structures of some stochastic gradient descent algorithms used in ANC: the filtered-x LMS, the adjoint-LMS and the modified filtered-x LMS. The new algorithms can be used in ANC systems or for the deconvolution of sounds in TSR systems. Also, heuristic techniques are introduced, to compensate for the potential ill-conditioning of the correlation matrix in ANC or TSR systems, and for the potential numerical instability of the multichannel FTF-based algorithms. Simulations of ANC and TSR systems will compare the performance of the different multichannel LMS, RLS, and FTF-based algorithms.

Active noise control of higher-order modes in a rectangular duct using stabilized fast transversal filters

For active noise control of sound propagating down a duct in the fundamental mode commercial systems are available. Cancellation of sound also propagating in higher-order modes adds the requirement of higher computational power for the signal processing unit, and stability problems due to source coupling effects. The widely used LMS algorithms need little computational effort, are very stable, but also have a slow tracking behavior to changes in the input signal. Depending on the eigenvalue spread of the input signal’s autocorrelation matrix they lead to slow convergence. One method to overcome this problem is to use stabilized fast RLS algorithms which are independent of the statistics of the input signal. A multi-channel stabilized fast transversal filter algorithm has been investigated experimentally in a rectangular duct with respect to its stability, convergence, and performance.

Fast square-root RLS adaptive filtering algorithms

In this paper two fast RLS adaptive filtering algorithms are described. Both algorithms compute the lattice coefficients and are based on the development of square-root factorizations of the autocorrelation matrix. Due to the square-root nature of the algorithms, the recursion is numerically stable. Experimental evaluations have been performed in limited precision environment, and comparison with the stabilized fast transversal filter algorithm (Slock and Kailath, 1991) has been made. Since the described algorithms require O( N) operations per sample, where N is the filter order, from a computational complexity point of view they represent a substantial advantage over the O( N 2 ) complexity of classical square-root algorithms.

A modified block FTF adaptive algorithm with applications to underwater target detection

In this paper, the problem of weighted block recursive least squares (RLS) adaptive filtering is formulated in the context of a block fast transversal filter (FTF) algorithm. This "modified block FTF algorithm" is derived by modifying the constrained block-LS cost function to guarantee global optimality. This new soft-constrained algorithm provides an efficient way of transferring weight information between blocks of data. The tracking ability of the algorithm can be controlled by varying the block length and/or a soft constrained parameter. This algorithm is computationally more efficient compared with other LS-based schemes. The effectiveness of this algorithm is tested on a real-life problem dealing with underwater target identification from acoustic backscatter. The process involves the identification of the presence of resonance in the acoustic backscatter from a target of unknown shape submerged in water.

Fast transversal versions of the RIV algorithm

The system of linear equations A(n)w(n)=b(n) where A(n) is the sample cross-correlation matrix between an observed process and an instrumental variable process and b(n) is the cross-correlation vector between some desired process and the instrumental variable process, is frequently encountered. For example, the ‘normal’ equations for the AR parameters of ARMA processes based on cumulants can be interpreted as cross-correlation matrices. For a p × p matrix A(n) the recursive instrumental variable (RIV) algorithm requires computations of order p2. We develop exact fast versions which require computations of order p. This is a generalization of the fast transversal filter algorithms of Cioffi et al., who assume the matrix A to be Hermitian. Additionally, we analyse the tracking behaviour and misadjustment aspects of RIV when λ, the forgetting factor, is less than unity.

A fast transversal filtering algorithm for pole-zero modeling

This paper describes a pole-zero (ARMA) modeling of discrete time linear systems ùsing a recursive least-squares (RLS) fast transversal filter (FTF) algorithm. This ARMA FTF algorithm is derived using geometric projections. The geometric projection approach gives insight and useful interpretation of various filters that form the algorithm. This algorithm can exactly estimate unknown filter coefficients. Simulation results are presented to show the rapid convergence speed and the numerical accuracy of the algorithm. We show that this algorithm converges more accurately than the ARNA FTF algorithm of Ardalan and Faber (1988). This algorithm also requires less computations than RLS lattice filters and the algorithm of Ardalan and Faber. Dieser Beitrag beschreibt eine Pol-Nullstellen (ARMA) Modellierung zeitdiskreter linearer Systeme mit einem schnellen rekursiven Least Squares (RLS) Transversalfilteralgorithms (FTF). Die Herleitung dieses ARMA-FTF-Algorithmus geschieht mit Hilfe geometrischer Projektionen. Der Ansatz basierend auf geometrischen Projektionen ermöglicht die Einsicht und eine nützliche Interpretation verschiedener Filter, welche im Algorithmus zusammenwirken. Der vorgestellte Algorithmus ermöglicht eine genaue Schätzung der unbekannten ARMA-Systemparameter. Die Simulationsergebnisse belegen die rasche Konvergenz und die numerische Stabilität des Verfahrens. Wir zeigen, daβ dieser Algorithmus genauer konvergiert als das ARMA-FTF-Verfahren von Ardalan und Faver (1988). Darüber hinaus erfordert das neue Verfahren einen geringeren Rechenaufwand als RLS-Lattice-Algorithmen und ebenfalls einen geringeren Rechenaufwand als das Verfahren von Ardalan und Faber. Cet article décrit un modèle pôles-zéros (ARMA) de systèmes linéaires à temps discret utilisant un algorithme rapide de filtre transversal (FTF) aux moindres carrés récursif (RLS). Cet algorithme ARMA FTF est dérivé à l'aide de projections géométriques. Cette approche de projection géométrique donne une meilleure vision et des interprétations utiles des divers filtres qui forment l'algorithme. Cet algorithme est capable d'estimer exactment des coefficients de filtre inconnus. Nous présentons des résultats de simulation pour montrer la rapidité de convergence et la précision numérique de l'algorithme. Nous montrons qu'il converge plus précisément que l'algorithme de filtrage ARMA FTF de Ardalan et Faber (1988). Il requièrt également moins de calculs que les algorithmes de filtre en treillis RLS et de Ardalan et Faber.

A numerically stable fast transversal filtering algorithm for pole-zero modelling

A numerically stable pole-zero (ARMA) modelling of discrete time linear systems is described using a recursive-least-squares (RLS) fast transversal filter (FTF) algorithm. This numerically stable ARMA FTF algorithm is derived using geometric projections and the error feedback procedure. This algorithm can exactly estimate unknown filter coefficients. Simulation results are presented to show the rapid convergence speed, numerical accuracy and stability of the algorithm. This algorithm is shown to converge more accurately and rapidly than the ARMA FTF algorithm of Ardalan and Faber (1988). The computaticnal requirements of this algorithm are compared with RLS lattice filters and the Ardalan-Faber algorithm.

Pole-zero modeling of speech using fast transversal filtering algorithm

This paper describes a pole-zero (ARMA) modeling of speech using a recursive-least-squares (RLS) fast transversal filter (FTF) algorithm. This ARMA FTF algorithm can estimate unknown input excitation and the estimated input is used to determined the parameters of the pole-zero model. This algorithm is derived using geometric projections. The geometric projection approach gives insight and useful interpretation of various filters that form the algorithm. We give a performance evaluation of the proposed algorithm by applying to synthetic and natural speech spectral estimations. This algorithm accurately represents spectral peaks and valleys of speech and requires less computations than RLS lattice filters and ARMA FTF algorithm of Ardalan and Faber (1988). Additionally, this algorithm can also be applied to other signal processing areas where the input is unknown.

Line search algorithms for adaptive filtering

Line search algorithms for adaptive filtering that choose the convergence parameter so that the updated filter vector minimizes the sum of squared errors on a linear manifold are described. A shift invariant property of the sample covariance matrix is exploited to produce an adaptive filter stochastic line search algorithm for exponentially weighted adaptive equalization requiring 3N+5 multiplications and divisions per iteration. This algorithm is found to have better numerical stability than fast transversal filter algorithms for an application requiring steady-state tracking capability similar to that of least-mean square (LMS) algorithms. The algorithm is shown to have faster initial convergence than the LMS algorithm and a well-known variable step size algorithm having similar computational complexity in an adaptive equalization experiment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A modular prewindowing framework for covariance FTF RLS algorithms

In a companion paper, a fast transversal filter (FTF) algorithm was derived for solving multichannel multiexperiment recursive least-squares (RLS) problems arising in adaptive FIR filtering. by introducing sequential processing of the different channels and experiments, the multichannel multiexperiment algorithm was decomposed into a set of interwined single-channel single-experiment algorithms, resulting in a modular algorithm structure. The algorithm was derived under the prewindowing assumption. However, using an embedding into multichannel and multiexperiment problems, we show how the conventional FTF algorithms for the growing-window and sliding-window covariance cases follow naturally from the modular prewindowed algorithm. Furthermore, taking the sequential processing one step of granularity further, we derive modular multichannel FTF algorithms for these covariance cases also. In einem zugehörigen Beitrag wurde ein Algorithmus zur schnellen Transversalfilterung (FTF) hergeleitet, welcher mehrkanalige Vielfach-Experiment-RLS-Probleme löst, wie sie bei der adaptiven Filterung auftreten. Durch die Einführung einer sequentiellen Verarbeitung der verschiedenen Kanäle und Experimente wurde der Mehrkanal-Vielfachexperiment-Algorithmus zerlegt in einen Satz verflochtener einkanaliger, auf ein Experiment bezogener Algorithmen, was zu einer modularen Struktur des Verfahrens führt. Der Algorithmus wurde unter der Annahme einer vorangehenden Fensterung hergeleitet. Indem wir jedoch eine Einbettung in mehrkanalige Vielfachexperiment-Probleme benutzen, können wir zeigen, wie übliche FTF-Verfahren für die Fälle einer Fensterung der Kovarianz mit wachsendem und mit gleitendem Fenster in natürlicher Weise aus dem modularen Algorithmus mit vorangehender Fensterung folgen. Weiterhin leiten wir, indem wir den Gedanken der sequentiellen Verarbeitung einen kleinen Schritt weiterführen, auch modulare Mehrkanal-FTF-Verfahren für diese Kovarianzfälle her. Nous avons dérivé dans un article associé un algorithme de filtre transversal rapide (FTF) pour la résolution de problémes aux moindres carrés récursifs (RLS) multi-canaux multi-expériences, nous avons décomposé l'algorithme multi-canaux multi-expériences en un ensemble d'algorithmes canal-unique expérience-unique entrelacés, avec pour résultat une structure algorithmique modulaire. Nous avons dérivé cette algorithme sous une hypothése de pré-fenêtrage. Nous montrons toutefois comment, en utilisant une immersion dans de problèmes multi-canaux multi-expériences, les algorithmes FTF conventionnels correspondant aux cas de type covariance à fenêtre croissante et fenêtre glissante résultent naturellement de l'algorithme modulaire pré-fenêtré. Nous dérivons également de plus, en entraînant le traitement séquentiel un pas de granularité plus loin, des algorithmes FTF multi-canaux modulaires pour ces cas de type covariance.

A modular multichannel multiexperiment fast transversal filter RLS algorithm

Abstract A Fast Transversal Filter (FTF) algorithm is proposed for solving multichannel multiexperiment Recursive Least-Squares (RLS) problems that exhibit a shift structure between consecutive regression vectors. The sequential processing of the different channels and experiments decomposes the multichannel multiexperiment algorithm into a set of intertwined single-channel single-experiment algorithms, resulting in a modular algorithm structure. The sequential processing strategy corresponds to a triangular factorization of error covariance matrices and numerical benefits accrue from this approach. Furthermore, recently introduced stabilization techniques for proper control of the propagation of numerical errors in the update recursions of FTF algorithms can also straightforwardly be incorporated. The algorithm is derived under the prewindowing assumption. In a companion paper we show how the proposed algorithm provides a framework of the covariance windowing cases.