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In order to ensure a good filterbank (FB) performance in cases where there are significant changes in the subband signals, the filters in such FBs must have very narrow transition bandwidths. When using conventional finite-impulse response (FIR) filters as building blocks for generating these FBs, this implies that their orders become very high, thereby resulting in a high overall arithmetic complexity. For considerably reducing the overall complexity, this contribution exploits the frequency-response masking (FRM) technique for synthesizing FIR filters for the above-mentioned FBs, where rational sampling factors are used. Comparisons between various optional methods of utilizing the FRM technique for designing FBs under consideration shows that the most efficient one, from both the design and the implementation viewpoints, are FBs that are constructed such that the bandedge-shaping or periodic filters are evaluated at the input sampling rate and the masking filters at the output sampling rate. This is shown by means of illustrative examples.