An integer-reversible MDCT transformation is split into consecutive lifting steps, each introducing considerable rounding errors to the signal. Without noise shaping the rounding error noise will impact all frequency bins of the transformed signal equally. This is a particular problem for low signal level frequency bins. The invention limits the impact of rounding error noise coming with each lifting step in the integer-reversible transformation on the data rate of a lossless audio codec. The filter coefficients of an adaptive noise shaping filter for transform coefficients are adapted in individual lifting steps according to the current time domain signal characteristics. As an alternative, an auto-regressive pre-filter can be added in front of the lossless transformation, for raising the level of frequency regions with low power to decrease the dominance of rounding errors in these areas. Both processes can be combined to further improve lossless codec compression ratio.