Abstract
In this paper we present a new method for the efficient implementation of the fast transversal filter(ftf) algorithm. Reduction of the arithmetic complexity is obtained by making use of the redundancy in the successive computations of the forward prediction error and the filtering error in the joint process. The resulting algorithm is exactly equivalent to the originalftf algorithm, hence retaining the same theoretical convergence characteristics and offering the least squares(ls) estimate at each recursion step without delay. Furthermore, the algorithm can be numerically stabilized by using a simple and effective stabilization measure which needs only one additional multiplication per recursion step. The equivalence of the proposed algorithm to the originalftf algorithm is demonstrated by simulations of an acoustic room impulse response identification.
Résumé
Cet article a pour objet de présenter une nouvelle méthode de mise αen uvre efficace de l’algorithme de filtre transversal rapide (ftf). La complexité arithmétique est réduite par redondance dans les calculs successifs de l’erreur de prédiction directe des signaux et de l’erreur dans l’estimation de la voie de filtrage des signaux. L’algorithme résultant équivaut exactement à l’algorithme ftf original, il possède les mêmes caractéristiques de convergence théoriques et permet aussi l’approximation par moindres carrés à chaque itération sans introduction de retard. En outre l’algorithme peut être stabilisé numériquement par une opération simple et efficace ne nécessitant qu’une seule multiplication supplémentaire pour chaque pas récursif. L’équivalence entre l’algorithme proposé et l’algorithme original est démontrée par simulation de l’identification de la réponse impulsionnelle d’une chambre anéchoïde.
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This work was supported by the Deutsche Bundespost Telekom.
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Ren, Z., Hartmann, I. & Schütze, H. A fast exact FTF adaptive algorithm. Ann. Télécommun. 49, 398–406 (1994). https://doi.org/10.1007/BF02999428
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DOI: https://doi.org/10.1007/BF02999428
Key words
- Transverse filter
- Adaptive algorithm
- Fast algorithm
- Algorithm complexity
- Estimation error
- Stabilization
- Echo canceller