The paper discusses computationally efficient NLMS and RLS algorithms for perfect and imperfect periodic excitation sequences. The most interesting aspect of these algorithms is that they are exact LMS 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 better than or comparable with the NLMS algorithm for white noise input. The transient and steady state behavior of the algorithms and their tracking properties are also studied in the paper.
