Wideband algorithms versus narrowband algorithms for adaptive filtering in the DFT domain

Adaptive filtering in the DFT domain is popular for its computational efficiency and its attractive convergence properties resulting from the applicability of the FFT and separate adaptation of individual DFT bins. Narrowband algorithms assume a complete decoupling of different frequency bins, which corresponds to assuming a circulant structure for the input data matrix. Wideband designs account for the difference between the actual Toplitz structure and the circulant structure by introducing additional constraints. In this contribution, we show that a wideband approach with rigorous implementation of appropriate constraints leads to highly efficient algorithms with excellent convergence properties. As examples we consider multichannel acoustic echo cancellation (MC-AEC) and blind source separation (BSS) of convolutive mixtures.