Integer fast modified cosine transform

In this paper, an efficient implementation of the forward and inverse MDCT is proposed for even-length MDCT. The algorithm uses discrete cosine transform of type II (DCT-II) to compute the forward MDCT and their inverse DCT-III to compute the inverse MDCT. The lifting scheme is used to approximate multiplications appearing in the MDCT lattice structure where the dynamic range of the lifting coefficients can be controlled by proper choices of the lifting factorizations. The new structure requires less multiplications and additions than previous reported algorithms. The new transform has the properties that it is an integer-to-integer mapping and is reversible. Moreover, it inherits most of the attractive properties of the MDCT, including a good spectral representation of the audio signal, critical sampling and overlapping of blocks. Hence, the intMDCT is suitable for both lossless and lossy audio coding.