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In this letter, a delayless counterpart of the partitioned frequency-domain adaptive filter algorithm is straightforwardly derived from the block least-mean-square (BLMS) algorithm. To improve its tracking capability, a time/frequency-domain unified (TFU) adaptation scheme is proposed. It is further shown that other delayless realizations can be seen as simplified implementations of the TFU technique. Simulations are presented to support the analyses and demonstrate the good convergence and tracking performance of the proposed algorithm.