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Based on a polyphase analysis of a subband adaptive filter (SAF) system, it is possible to calculate the optimum subband impulse responses to which the SAF system will converge. We give some insight into how these optimum impulse responses are calculated, and discuss two applications of our technique. Firstly, the performance limitations of an SAF system can be explored with respect to the minimum mean square error performance. Secondly, fullband impulse responses can be correctly projected into the subband domain, which is required for example for translating constraints for subband adaptive beamforming. Examples for both applications are presented.