New block filtered-X LMS algorithms for active noise control systems

New block formulations for an active noise control (ANC) system using only convolution machines are presented. The proposed approaches are different from conventional block least-mean-square (LMS) algorithms that use both convolution and cross-correlation machines. The block implementation is also applied to the filtering of the reference signal by the secondary-path estimate. In addition to the use of the fast Fourier transform (FFT), the fast Hartley transform (FHT) is used to develop transform-domain ANC structures for reducing computational complexity. In the proposed approach, some FFT and FHT blocks are removed to obtain an additional reduction of the computational burden resulting in the reduced-structure of FFT-based block filtered-X LMS (FBFXLMS) and FHT-based block filtered-X LMS (HBFXLMS) algorithms. The computational complexities of these new ANC structures are evaluated.