Approximation error analysis for transform-based lossless audio coding

The Integer Modified Discrete Cosine Transform (IntMDCT), an integer approximation of the MDCT, is a reversible transform realized by the lifting scheme and thus is a useful transform for lossless audio coding. Because of the integer approximation, however, the approximation error appears as "noise floor" in the transform domain and limits the lossless coding efficiency. In this paper, a theoretical analysis of the approximation error of the IntMDCT is discussed. The result is then used to design a simple test filter applied to each founding operation of the IntMDCT in such a way that the error spectrum is shaped towards the low frequencies. As a result, especially when the spectral energy of an input signal is concentrated in the low frequency domain, the lossless coding efficiency is improved.