Fast multidelay block transform-domain adaptive filters based on a two-dimensional optimum block algorithm

Three fast and flexible block transform-domain gradient adaptive digital filters (ADF´s) for finite impulse response (FIR) adaptive filtering are presented. The proposed ADF´s employ a two-dimensional optimum block algorithm (OBA) in order to obtain a time-varying convergence factor which is optimized in a least square (LS) sense for fast and accurate adaptation, and to allow one to choose an appropriate transform size for smaller block delay and more efficient use of a hardware. In the first one of the proposed ADF´s, the multidelay frequency-domain OBA (MFOBA), the two-dimensional OBA is realized with the conventional fast Fourier transform (FFT). In the second one, the normalized MFOBA (NMFOBA), a robust normalization method significantly improves its convergence speed for colored input signals. In the third one, the Fermat number transform (FNT) based realization (MFOBA/FNT), the desirable properties of the FNT (e.g., no roundoff errors, no multiplication and no complex basis functions) are utilized to yield an ideal structure for an efficient hardware implementation. By computer simulation, it is shown that these ADF´s are faster than other transform-domain adaptive algorithms