Convergence analysis of an adaptive filtering structure using a new adaptation scheme

The convergence analysis of a maximally decimated (MD) adaptive filtering structure (AFS) employing a new adaptation scheme is presented. The structure was based on uniform perfect reconstruction (PR) filter banks (FB), their dual transmultiplexers (TMUX) and a model for the system under identification of interpolated FIR (IFIR) filters connected in parallel. A new algorithm was used for the adaptation of the subband filter coefficients employing a new power normalisation (PN) scheme introduced in Papoulis et al. (2002). This structure is briefly described here, the adaptive algorithm is presented and an extensive convergence analysis is then given. Reference then is made to the relevant work reported in Petraglia et al. (2000), namely to a structure that can be considered as the dual of the one presented here and employed an adaptive algorithm that is a simplified version of the one we proposed. The convergence analysis is then specialised for the adaptive scheme used in Petraglia. The rest of the paper is an extensive performance comparison of both structures and of the two adaptation schemes, through both theoretical and experimental results. These demonstrate the improvement in the performance our approach offers; highlight aspects of the theoretical analysis and further enlighten on the similarities and differences of the two approaches. A performance comparison with the full-band NLMS algorithm is given.