A constrained transform domain adaptive IIR filter structure for active noise control

An active noise controller utilizing a transform domain recursive LMS (RLMS) infinite impulse response (IIR) filter is presented in this paper. The new filter, termed the TRLMS adaptive filter, mitigates the filter instability problems that often exist with controllers based on direct form IIR filters by directly constraining the adaptation of the filter´s frequency response. A filtered-U adaptive algorithm for the TRLMS filter structure is derived. Two different implementations of the constrained TRLMS filter are discussed. The first represents the adaptive filter in terms of its transform domain weights. They are directly adapted by the filtered-U TRLMS adaptive algorithm. The second implementation represents the filter in terms of its original time domain weights. These are updated by the filtered-U RLMS algorithm and subsequently projected onto an adaptation subspace at each iteration. Extensions of these algorithms that enforce soft constraints on the filter response are also presented. The stability of the constrained TRLMS adaptive filter is investigated utilizing two different transformations