Regressive implementations for the forward and inverse MDCT in MPEG audio coding

Modified discrete cosine transform (MDCT) and inverse modified discrete cosine transform (IMDCT) are two of the most compute-intensive operations in layer III of the MPEG audio coding standard. We first derive two sinusoidal recursive formulas for the transform kernels of the MDCT and IMDCT. Then we demonstrate that general length of MDCT and IMDCT can be efficiently implemented by using the regressive structure derived from the sinusoidal recursive formulas. The proposed regular structure is particularly suitable for parallel VLSI realization. Besides, it also provides an efficient on-line computation scheme and is especially suitable for the computation of variable length MDCT and IMDCT when involving dynamical window switching in the MPEG audio coding standard.