Low complexity and fast computation for recursive MDCT and IMDCT algorithms

Fast algorithms are derived for modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) in this brief. The proposed algorithms based on type II discrete cosine transform and type II discrete sine transform not only adopt a unified architecture for both MDCT and IMDCT computations but also take only N/8 + 1 computational cycles for each output sequence. Compared with previous IMDCT approaches, the number of preprocessing multiplications of the proposed IMDCT algorithm is reduced by 87.5%. In addition, the coefficient requirements for preprocessing in the proposed IMDCT algorithm can be reduced by 50%, and the number of multiplications for the recursive kernel is greatly decreased by up to 87.5%. The proposed algorithms in terms of hardware costs take two fewer multipliers and six fewer adders than some well-known recursive algorithms. Therefore, the proposed architecture is better suited for various audio codecs.