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A novel method of the computation of the discrete fractional cosine transform (DFRCT) based on adaptive Least Mean Square (LMS) algorithm is proposed. The weight vectors are adjusted or adapted in accord with the least mean square error between the ldquodesired responserdquo and the reconstructed signal. It can be proved that the weight vector is in relation to the previous N-point DFRCT by choosing the iterative index properly. Theoretical analysis and simulation results show that the performance of the proposed algorithm is very close to that of Pei, and also it is simple in computation.