Fast IMDCT and MDCT algorithms - a matrix approach

This paper presents a systematic investigation of the modified discrete cosine transform/inverse modified discrete cosine transform (MDCT/IMDCT) algorithm using a matrix representation. This approach results in new understanding of the MDCT/IMDCT, enables the development of new algorithms, and makes clear the connection between the algorithms. We represent in a matrix form the IMDCT as the product of the type-IV DCT with simple scaling, sign-changing, and permutation operations such that fast algorithms for the type-IV DCT can be simply modified for the IMDCT, and vice versa. Then, the simple symmetry and inversion properties of the type-IV DCT are used to develop new algorithms and establish the connection between existing fast IMDCT algorithms. This approach also enables us to show that MDCT and IMDCT share common core operation and present an efficient architecture for implementing both the MDCT and the IMDCT in one hardware.