On the Performance Analysis of Normalized Subband Adaptive Filtering Algorithm with Sparse Subfilters

Abstract

Subband adaptive filtering algorithms can increase the convergence rate of system identification tasks when the input signal is colored. Recently, a new normalized subband adaptive filtering algorithm with sparse subfilters (NSAF-SF) has been proposed, whose main advantage is the lower computational complexity when compared to state-of-the-art subband approaches, while maintaining similar convergence performance. In this paper, the first- and second-order stochastic analyses of the NSAF-SF algorithm are presented in order to provide predictions about its transient and steady-state performances. A relationship between the adaptive subband coefficients and the ideal fullband transfer function is derived, and the algorithm is proven to produce an asymptotically unbiased solution. In addition, a closed-form expression is obtained for the steady-state mean square deviation (MSD) of the subfilter coefficients. Although the proposed analyses use conventional assumptions of statistical independence, they do not assume a specific stochastic characteristic for the input signal (e.g., Gaussianity or whiteness). Transient and steady-state theoretical predictions of the MSD are confirmed by simulations.