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Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper.