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In a typical conventional narrowband ANC system, the discrete Fourier coefficients (DFC) for each frequency are estimated by a linear combiner. Each reference (cosine or sine) wave has to be filtered by an estimate of the secondary-path before it is fed to the LMS algorithm. We call this part x-filtering block. The number of x-filtering blocks is 2q where q is the number of targeted frequencies. For larger q and/or higher order (M) of estimated FIR-type secondary-path, the computational cost due to x-filtering may become a bottleneck in real system implementation. Here, we propose a new narrowband ANC system structure which requires only two (2) x-filtering blocks regardless of q. All the cosine waves (or sine waves) are combined as an input to a x-filtering block. The output of this block is decomposed by an efficient bandpass filter bank into filtered-x cosine or sine waves for the FXLMS that follows. The computational cost of the new system is significantly reduced especially for large q and/or M. The new structure is also modified to cope with the frequency mismatch (FM). Simulations demonstrate that the new systems present performance which is very similar to that of the conventional system, but enjoy great advantages in system implementation.