Mean-Square Performance Analysis of the Normalized Subband Adaptive Filter

This paper presents the mean-square performance analysis of a class of normalized subband adaptive filters (NSAF) using the concept of energy conservation. The NSAF has a unique weight-control mechanism whereby subband error signals are used to update a fullband tap-weight vector. We show that an energy conservation relation can be established for the weight adaptation. Subsequently, an expression for the steady-state excess mean-square error (MSE) and the necessary condition on the step size for mean-square stability can then be derived by manipulating various error quantities of the energy conservation relation. Simulation results are presented to corroborate the mathematical analysis.