A unified approach to time- and frequency-domain realization of FIR adaptive digital filters

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 [1]-[12], [16]-[18] 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.