This paper proposes an effective method for converting any fast DCT algorithm into an approximate multiplierless version. Basically it approximates any constant in the original transform by a signed digit representation. We developed an efficient algorithm to convert any constant into a signed digit string with a minimum number of non-zero signed digits and a reduced length. As the accuracy of an approximated algorithm depends critically on the assignment of signed digits to the constants, this paper formulated an effective algorithm for finding an effective signed digits configuration which could minimize the MSE of an approximated DCT algorithm with a specified complexity. Experiment results show that the AAN's fast DCT algorithm, approximated by the proposed method and using an optimized configuration can be used to reconstruct images with high visual quality in terms of PSNR.