Steady-State Performance Limitations of Subband Adaptive Filters

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Description/Abstract

Non-perfect filter banks used for subband adaptive filtering (SAF) are known to impose limitations on the steady-state performance of such systems. In this paper, we quantify the minimum mean-square error (MMSE) and the accuracy with which the overall SAF system can model an unknown system that it is set to identify. Firstly, in case of MMSE limits, the error is evaluated based on a power spectral density description of aliased signal components, which is accessible via a source model for the subband signals that we derive. Approximations of the MMSE can be embedded in a signal-to-alias ratio (SAR), a factor by which the error power can be reduced by adaptive filtering. With simplifications, SAR only depends on the filter banks. Secondly, in case of modelling, we link the accuracy of the SAF system to the filter bank mismatch in perfect reconstruction. When using modulated filter banks, both error limits --- MMSE and inaccuracy --- can be linked to the prototype. We explicitly derive this for generalized DFT modulated filter banks and demonstrate the validity of the analytical error limits and their approximations for a number of examples, whereby the analytically predicted limits of error quantities compare favourably with simulations.