Transient Analysis of Adaptive Filters Using a General Framework

Employing a recently introduced framework in which a large number of adaptive filter algorithms can be viewed as special cases, we present a generalized transient analysis. An important implication of this is that while the theoretical analysis is performed for a generic filter coefficient update equation the results are directly applicable to a large range of adaptive filter algorithms simply by specifying some parameters of this generic filter coefficient update equation. In particular we point out that theoretical learning curves for the Least Mean Square (LMS), Normalized Least Mean Square (NLMS), the Affine Projection Algorithm (APA) and its relatives, as well as the Recursive Least Squares (RLS) algorithm are obtained as special cases of a general result. Subsequently, the recently introduced Fast Euclidian Direction Search (FEDS) algorithms as well as the Pradhan-Reddy subband adaptive filter (PRSAF) are used as non-trivial examples when we demonstrate the usefulness and versatility of the proposed approach to adaptive filter transient analysis through an experimental evaluation.

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