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Specific implementations of the finite impulse response (FIR) block adaptive filter in the frequency domain are presented and some of their important properties are discussed. The time-domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency-domain adaptive filter (derived in the frequency domain), provided data sectioning is done properly. All of the known time- and frequency-domain adaptive filters -, - are contained in the set of possible block adaptive filter structures. Thus, the block adaptive filter is generic and its formulation unifies the current theory of time- and frequency-domain FIR adaptive filter structures. A detailed analysis of overlap-save and overlap-add implementations shows that the former is to be preferred for adaptive applications because it requires less computation, a fact that is not true for fixed coefficient filters.