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A new narrowband ANC system structure is proposed which requires only two reference signal filtering (x-filtering) blocks regardless of the number of targeted frequencies. The reference cosine or sine waves are combined, respectively, to form an input to an x-filtering block. The output of each x-filtering block is decomposed into filtered-x cosine or sine waves by a special bandpass filter bank. In this way, the computational cost of the system may be significantly reduced. Analysis of the new system is then provided and discussed in some detail. Analytical results reveal that the proposed system performs quite the same as its counterpart does while requiring considerably fewer multiplications. Modification to the proposed structure is also made to cope with the frequency mismatch (FM) in real-life applications. Extensive simulations are conducted to demonstrate the effectiveness of the proposed system and its modified version, and as well as to confirm the validity of analysis.