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This paper studies the design of frequency response masking (FRM) filters with infinite duration impulse response (IIR) model and masking sub-filters. They are useful in realizing sharp cutoff digital filters and with low passband delays. The designs of the model and masking filters are carried out by means of semidefinite programming (SDP) and model order reduction. Design results show that low complexity FRM filters with low passband delay can be obtained.