Nowadays speech processing methods are usually implemented in the time or frequency domain. Filter bank can be considered as a divide and conquer approach within signal processing, since large problems are sub-divided into many smaller problems. While filter banks are essential components of speech processing, and in signal processing in general, they will have the focus in present days. An adaptive filter is a filter that self adjusts its transfer function according to its optimizing algorithms. Least mean square algorithm has slow convergence when used with nonstationary signals like speech and it has high computational cost but normalization of step size (or input signal) leads to a useful variant of the LMS algorithm known as the normalized LMS (NLMS) algorithm, which gives better convergence characteristics than the LMS because it uses a variable step-size with respect to the input signal power. To improve the convergence rate and/or computational complexity and also to overcome the disadvantage of a full band adaptive filtering, a structure is illustrated that is subband adaptive filtering; this will converge faster at a lower computational cost for speech and white noise inputs. This research shows most types of subband decomposition structures and makes comparison among them based on their performance to cancel the noise with minimum computational complexity, maximum convergence speed and maximum noise cancellation with lowest delay. Moreover three new hybrid tree configurations or the tree decom-position are proposed to maximize the overall performance of adaptive noise cancellation system .They are given the abbreviations HTPSAF1,HTPSAF2 and HTPSAF3. These three systems use polyphase filter bank that has showed a noticeable increase in the convergence speed and large reduction in the computational complexity due to the lower number of coefficients that can be achieved for the analysis/synthesis filters, which in turn will result in minimum delay in the reconstructed output speech signal. The algorithm of subband decomposition structures has been described theoretically then modeled under MATLAB simulation program using built-in filters and real input signals.