  In order to improve the performances of recently-presented improved
normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms
for highly noisy system, this paper proposes their set-membership versions by
exploiting the theory of set-membership filtering. Apart from obtaining smaller
steady-state error, the proposed algorithms significantly reduce the overall
computational complexity. In addition, to further improve the steady-state
performance for the algorithms, their smooth variants are developed by using
the smoothed absolute subband output errors to update the step sizes.
Simulation results in the context of acoustic echo cancellation have
demonstrated the superiority of the proposed algorithms.
