On the performance analysis and applications of the subband adaptive digital filter

Abstract In this paper, the performance analysis of the subband adaptive digital filter (SBADF) is provided, and it is shown that the SBADF provides better performance than the conventional full band adaptive digital filter (FBADF) in some applications. First, we derive the optimum filter for each subband in terms of the given input statistics, and also derive the relationship between the optimum filter for each subband and that of the FBADF. Second, the autocorrelation function of the signals in each subband is derived to investigate the tap weight behavior and the mean square error of the SBADF. The autocorrelation function is expressed in terms of the input statistics, from which the eigenvalue spreads of the SBADF and the FBADF can be examined, provided that the filter length is sufficiently long. Third, for investigating the convergence behavior, we provide analytical expressions for the error surface of SBADF. Finally, we employ the SBADF for adaptive line enhancer and adaptive equalizer to demonstrate that the SBADF performs better than the FBADF, provided that the power spectrum of the input to the adaptive filter is not uniformly distributed.

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