Multilevel split-path adaptive filtering and its unification with discrete Walsh transform adaptation

It has been shown that the convergence speed of an adaptive transversal filter can be made faster if the filter is split into a pair of symmetric/antisymmetric linear phase subfilters. In this brief, a generalized multilevel splitting approach is proposed which enables the realization of a modular split-path adaptive filter. It is demonstrated that an LMS FIR filter of length 2L, where L is an integer, can be decomposed into a set of parallel single-parameter subfilters by a novel L-step splitting procedure. The convergence behavior of the new filter configuration is improved noticeably and is confirmed experimentally. A unified perspective of the multilevel split-path adaptive filtering method with the discrete Walsh transform adaptation is also established.