This paper presents a shared architecture design for computations of Discrete Fourier Transform (DFT), Inverse DFT (IDFT), and Inverse Modified Cosine Transform (IMDCT) algorithms. The proposed method has following advantages, such as 1) Low hardware costs compared with conventional recursive DFT (RDFT) and recursive IDFT (RIDFT) algorithms. For hardware implementation, 2 real multipliers and 8 real adders are required in the proposed architecture. Compared with previous approaches, it can greatly reduce 80% of number of multipliers and 53% of number of adders. 2) The proposed RDFT-based IMDCT architecture has four times data throughput more than the other existing recursive algorithm 3) Computational cycles of the proposed RDFT-based IMDCT algorithm can be greatly reduced by 50% more than our previous recursive IMDCT algorithms. Hence, the proposed RDFT / RIDFT / RDFT-based IMDCT design is more suitable for portable devices in Digital Radio Mondiale (DRM) system.