Filtered-X Affine Projection Algorithms for Active Noise Control Using Volterra Filters
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Filtered-X Affine Projection Algorithms for Active Noise Control Using Volterra Filters Alberto Carini Institute of Science and Information Technologies, University of Urbino, 61029 Urbino, Italy Email: [email protected]
Giovanni L. Sicuranza Department of Electrical, Electronic and Computer Engineering, University of Trieste, 34127 Trieste, Italy Email: [email protected] Received 1 September 2003; Revised 22 December 2003 We consider the use of adaptive Volterra filters, implemented in the form of multichannel filter banks, as nonlinear active noise controllers. In particular, we discuss the derivation of filtered-X affine projection algorithms for homogeneous quadratic filters. According to the multichannel approach, it is then easy to pass from these algorithms to those of a generic Volterra filter. It is shown in the paper that the AP technique offers better convergence and tracking capabilities than the classical LMS and NLMS algorithms usually applied in nonlinear active noise controllers, with a limited complexity increase. This paper extends in two ways the content of a previous contribution published in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP ’03), Grado, Italy, June 2003. First of all, a general adaptation algorithm valid for any order L of affine projections is presented. Secondly, a more complete set of experiments is reported. In particular, the effects of using multichannel filter banks with a reduced number of channels are investigated and relevant results are shown. Keywords and phrases: active noise control, adaptive Volterra filters, affine projection algorithms.
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INTRODUCTION
Methods for active noise control are nowadays intensively studied and have already provided promising applications in vibration and acoustic noise control tasks. The initial activities originated in the field of control engineering [1, 2], while in recent years a signal processing approach has been successfully applied. This approach strongly benefited of the advances in electroacoustic transducers, flexible digital signal processors, and efficient adaption algorithms [3, 4]. The technique used in a single-channel active noise controller is based on the destructive interference in a given location of the noise produced by a primary source and the interfering signal generated by a secondary source. Most of the studies presented in the literature refer to linear models, while it is often recognized that nonlinear effects can affect actual applications [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Such effects may arise from the behavior of the noise source which rather than a stochastic process may be depicted as a nonlinear deterministic noise process, sometimes of chaotic nature. Moreover, the primary path may exhibit a nonlinear behavior thus motivating the use of a nonlinear controller. Recently, a model for a nonlinear controller based on Volterra filters [15] has been presented in [9] with interest-
ing results. The model actually exploits the so-called diagonal representation introduced in [
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