Normalized Subband Adaptive Filter with Subband Selection

Abstract

In this thesis, we develop novel adaptive filters with subband adaptive filtering. Conventional subband adaptive filters do not use the filters efficiently. So, we provide the scheme to partially use the subband filtering and how to find the most effective subband filters. By the selection scheme, we can control the subband filters and computational complexity. Controlling subband filters is directly related to the convergence performance of adaptive filter. We introduce fundamentals of adaptive filtering. Start with Wiener filter and steepest descent method, we explain least-mean square (LMS) and normalized LMS (NLMS). We also explain subband adaptive filter (SAF) and focus on normalized subband adaptive filter (NSAF) which applied SAF to NLMS. First, we show a novel NSAF which automatically select subbands every iteration. Subband selection shows possiblity of reducing computational complexity. By the proposed subband selection, convergence performance is preserved as same as full subband. The number of subband is an important factor of convergence speed of NSAF. With many subbands, the convergence speed improves but the computational burden become heavier. This idea is come from the discrepancy between the subbands. Not all the subband can help to make the NLMS has better performance. We observe the input and output error signal to distinguish the fine subband. The experimental results show that the proposed algorithm has similar convergence speed as conventional NSAF. Computational complexity is much lower than that of conventional NSAF because of only a subset of subband are used. Second, we introduce another approach to improve the NSAF. Computational complexity problem can be solved by the first approach. We wanted to improve the convergence speed by the selection. We proposed a selective scheme that preserve the computational complexity but having better convergence speed. A characteristic of subband filtering is used. The number of subbands directly related to the convergence speed. If we use the subband filters that have large number of subbands, we can get faster convergence speed. Using different subband filters meas that the over all computational complexity is different. So, we calculate the computational complexity and control the subband selection not to have more computational burden. In conclusion, we can get better convergence speed without additional computational complexity by combination of subband extension and selection. We also derive another strategy of subband selection that maximize the convergence performance. Experimental results show that the proposed algorithm have faster convergence performance than conventional NSAF.