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This paper presents a very low-complexity design of variable bandedge linear phase finite-impulse-response (FIR) filters with fixed sharp transition width. The idea is to first decompose the input signal into several channels in the frequency domain. The channel(s) involved with the transition band of the variable filter due to the variation of the bandedge is (are) shaped to produce the required transition band, and then summed up with the channels involved with the passband of the variable filter to produce the required frequency response. The proposed variable filter has extremely low complexity when the transition band is sharp, if compared with other techniques such as the Farrow structure. It is possible that the computational complexity of the variable filter is even lower than that of a corresponding fixed filter with the same transition width and ripple specifications implemented in its direct form.