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Subband techniques have been recently developed for adaptive filters, since some of the applications such as acoustic echo cancellation and wideband active noise control need adaptive filters with thousands of taps, which result in high computational complexity and low convergence rate. By using subband adaptive algorithms, both computational complexity and convergence rate may be reduced. This paper presents a convergence analysis of a recently proposed subband adaptive structure with critical sampling, where the performance concerning the mean square error of the adaptive algorithm is superior to the results obtained so far for computationally efficient subband structures. Theoretical expressions for the steady-state mean coefficient vector and for the minimum and excess mean-square errors are derived, taking into account the residual aliasing in the subband structure. Computer simulations are presented in order to verify the theoretical results.