Improved integer transforms using multi-dimensional lifting [audio coding examples]

Recently lifting-based integer transforms have received much attention, especially in the area of lossless audio and image coding. The usual approach is to apply the lifting scheme to each Givens rotation. Especially in the case of long transform sizes in audio coding applications, this leads to a considerable approximation error in the frequency domain. This paper presents a multidimensional lifting approach for reducing this approximation error. In this approach, large parts of the transform are calculated without rounding operations, only the output is rounded and added. The new approach is applied and evaluated for both the integer modified discrete cosine transform (IntMDCT) and the integer fast Fourier transform (IntFFT).