Efficient NLMS and RLS algorithms for perfect periodic sequences

The paper discusses computationally efficient NLMS and RLS algorithms for perfect periodic excitation sequences. The most interesting aspect of these algorithms is that they are exact NLMS and RLS algorithms suitable for identification and tracking of every linear system and they require a real-time computational effort of just a multiplication, an addition and a subtraction per sample time. Moreover, the algorithms have convergence and tracking properties that can be comparable to or even better than the NLMS algorithm with a white noise input. The transient and steady state behavior of the algorithms is also studied in the paper.