Mean-square analysis of multi-sampled multiband-structured subband filtering algorithm

Although the multiband-structured subband adaptive filter (MSAF) and its convergence analysis have been widely studied, the existing analyses are carried out only in the decimated time domain. In this paper, we present a new theoretical mean-square analysis of the multi-sampled MSAF (MS-MSAF) algorithm in the original time domain, whereas the MS-MSAF algorithm extends the original sub-sampled number to a general value. Both the transient and steady-state performances are investigated, which provides a guideline for increasing the convergence rate of the MSAF. Then, the tracking ability is studied in a non-stationary environment. Moreover, the approximative analytical minimum mean-square deviation and optimum step size are derived. Simulation results illustrate the derived performance expressions, which show that there is a relatively good match between theory and practice.