Integer MDCT with enhanced approximation of the DCT-IV

Integer transform plays an important role in lossless signal compression. In order to achieve high accuracy to its corresponding theoretical transform, the rounding number should be as low as possible. At the same time, the matrix factorization for reversible integer mapping should be handled with care, especially when the processing block length is high (N>16). In this correspondence, a new method for realizing reversible integer discrete cosine transform type IV (DCT-IV) is proposed that is a key component used in audio compression. The proposed method exhibits low rounding number (2.5N) and low complexity O(Nlog₂N) as well as well as accurately represents its counterpart floating-point DCT-IV transformation.