Recently, proportionate adaptive algorithms have been proposed to speed up convergence in the identification of sparse impulse response. Although they can improve convergence for sparse impulse responses, the steady-state misalignment is limited by the constant step-size parameter. In this article, based on the principle of least perturbation, we first present a derivation of normalized version of proportionate algorithms. Then by taking the disturbance signal into account, we propose a variable step-size proportionate NLMS algorithm to combine the benefits of both variable step-size algorithms and proportionate algorithms. The proposed approach can achieve fast convergence with a large step size when the identification error is large, and then considerably decrease the steady-state misalignment with a small step size after the adaptive filter reaches a certain degree of convergence. Simulation results verify the effectiveness of the proposed approach.

Visual adaptation is a universal phenomenon associated with human visual system. This adaptation affects not only the perception of low-level visual systems processing color, motion, and orientation, but also the perception of high-level visual systems processing complex visual patterns, such as facial identity and expression. Although it remains unclear for the mutual interaction mechanism between systems at different levels, this issue is the key to understand the hierarchical neural coding and computation mechanism. Thus, we examined whether the low-level adaptation influences on the high-level aftereffect by means of cross-level adaptation paradigm (i.e. color, figure adaptation versus facial identity adaptation). We measured the identity aftereffects within the real face test images on real face, color chip and figure adapting conditions. The cross-level mutual influence was evaluated by the aftereffect size among different adapting conditions. The results suggest that the adaptation to color and figure contributes to the high-level facial identity aftereffect. Besides, the real face adaptation obtained the significantly stronger aftereffect than the color chip or the figure adaptation. Our results reveal the possibility of cross-level adaptation propagation and implicitly indicate a high-level holistic facial neural representation. Based on these results, we discussed the theoretical implication of cross-level adaptation propagation for understanding the hierarchical sensory neural systems.