TY - JOUR

T1 - A new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control systems

AU - Montazeri, Allahyar

AU - Poshtan, Javad

PY - 2011/1

Y1 - 2011/1

N2 - Infinite impulse response filters have not been used extensively in active noise and vibration control applications. The problems are mainly due to the multimodal error surface and instability of adaptive IIR filters used in such applications. Considering these, in this paper a new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control applications is proposed. At first an RLS-based adaptive IIR filter with computational complexity of order O(n(2)) is derived, and a sufficient condition for its stability is proposed by applying passivity theorem on the equivalent feedback representation of this adaptive algorithm. In the second step, to reduce the computational complexity of the algorithm to the order of O(n) as well as to improve its numerical stability, a fast array implementation of this adaptive IIR filter is derived. This is accomplished by extending the existing results of fast-array implementation of adaptive FIR filters to adaptive IIR filters. Comparison of the performance of the fast-array algorithm with that of Erikson's FuLMS and SHARF algorithms confirms that the proposed algorithm has faster convergence rate and ability to reach a lower minimum mean square error which is of great importance in active noise and vibration control applications.

AB - Infinite impulse response filters have not been used extensively in active noise and vibration control applications. The problems are mainly due to the multimodal error surface and instability of adaptive IIR filters used in such applications. Considering these, in this paper a new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control applications is proposed. At first an RLS-based adaptive IIR filter with computational complexity of order O(n(2)) is derived, and a sufficient condition for its stability is proposed by applying passivity theorem on the equivalent feedback representation of this adaptive algorithm. In the second step, to reduce the computational complexity of the algorithm to the order of O(n) as well as to improve its numerical stability, a fast array implementation of this adaptive IIR filter is derived. This is accomplished by extending the existing results of fast-array implementation of adaptive FIR filters to adaptive IIR filters. Comparison of the performance of the fast-array algorithm with that of Erikson's FuLMS and SHARF algorithms confirms that the proposed algorithm has faster convergence rate and ability to reach a lower minimum mean square error which is of great importance in active noise and vibration control applications.

KW - LMS ALGORITHM

KW - AFFINE

KW - Active noise and vibration control

KW - Adaptive IIR filters

KW - CONVERGENCE ANALYSIS

KW - SOUND REPRODUCTION SYSTEMS

KW - Recursive least square

KW - CANCELLATION

KW - LEAST-SQUARES ALGORITHMS

KW - Stability

KW - Fast array algorithm

U2 - 10.1016/j.sigpro.2010.06.013

DO - 10.1016/j.sigpro.2010.06.013

M3 - Journal article

VL - 91

SP - 98

EP - 113

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

IS - 1

ER -