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 a "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 rounding 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.