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In this paper, a new method for the design of optimal finite-impulse response frequency-response masking (FRM) filters with reduced passband group delays is proposed. To meet the prescribed magnitude response and group delay, the proposed design method takes into account both the magnitude error and the group delay error. The key step is the derivation of the group delay and its gradient with respect to the filter coefficients, based on which an explicit group delay constraint is formulated. By incorporating the group delay constraint into the overall optimization, FRM filters with better approximation to the prescribed reduced group delay can be obtained in comparison with a method by Lu and Hinamoto in 2003, as illustrated by two design examples.