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Frequency-response masking (FRM) approach is a very efficient method for designing linear-phase FIR digital filters with general passbands and sharp transition bands. The FRM approach has recently been adapted to design cosine-modulated filter banks (CMFB). The resulting structure is a two-stage filter formed by the polyphase decomposition of the base filter in cascade with the decomposition of the masking filter. The present paper discusses the implementation of the FRM-CMFB using a butterfly-type structure proposed by Malvar (1991) to implement the masking filter polyphase decomposition. The result is an even more efficient structure in terms of computational complexity. The issue of perfect reconstruction (PR) in this new structure is also addressed, and it is shown how the PR of the overall filter depends on the characteristics of the FRM base and masking filters.