Fast and lossless implementation of the forward and inverse MDCT computation in MPEG audio coding

The modified discrete cosine transform (MDCT) is a lapped transform used in transform coding schemes as an analysis/synthesis filter bank based on the concept of time domain aliasing cancellation. We propose to implement the MDCT using the lifting scheme for its lossless implementation with integer coefficients. The lifting scheme requires that the MDCT structure be composed of orthonormal matrices. In this paper we obtain the orthonormal factorization of the rotations and the DCT/DST blocks of the MDCT. The new MDCT structure obtained is then implemented using the lifting scheme. This renders the MDCT impervious to quantization errors making it a lossless scheme, in the sense that any quantization error introduced by the forward transform is removed by the inverse transform. A performance comparison of the proposed implementation and the current technique is presented