A statistics study of the MDCT coefficient distribution for audio

The modified discrete cosine transform (MDCT) has been widely used in many transform audio coding algorithms such as MPEG-1/2 layer III (mp3), MPEG-2/4 AAC, Dolby AC2/AC3, and numerous experimental audio coding algorithms. In this paper, we study the probabilistic distribution properties of the MDCT coefficient for audio signals. It is shown that the generalized Gaussian function with distribution parameter r=0.5 or r=1 (Laplacian) provides a good approximation to the distributions of MDCT coefficients for a variety of audio signals. Results from our study also show that although the distribution of these coefficients is not strictly Laplacian, the divergence between them is in fact very small. Therefore, it leads to only marginal redundancy if these coefficients are simply coded with some low-complexity codes designed for Laplacian sources