Stochastic model for the NSAF algorithm considering slow adaptation and Gaussian data

This paper proposes a stochastic model for the normalized subband adaptive filters (NSAFs), considering slow adaptation and Gaussian input signals. Such a filter structure is an alternative to the classical full-band normalized least-mean-square (NLMS) algorithm, aiming to improve the convergence speed under correlated input data. Analytical models for the first moment of the adaptive filter weight vector and the learning curve are derived. For such, the time-varying nature of the normalized step-size parameter as well as a regularization factor, which prevents division by zero during the normalizing operation, are taken into account. Through numerical simulations the accuracy of the proposed model is confirmed.