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The paper presents an optimized algorithm for the computation of the modified discrete cosine transform (MDCT) and its inverse transform (IMDCT). The proposed algorithm is based on the type II DCT (DCT-II). By extracting a common transform kernel to compute both the MDCT and IMDCT, we obtain a unified structure for computation of both of them. Also, since the proposed unified structure is very symmetrical, it is suited to the parallel or pipelined VLSI implementation of MDCT/IMDCT. Furthermore, it requires less calculation complexity than existing algorithms.