The corrupted speech is given by:
Thus, the relationship between speech and noise is non-linear one, as given in Eq.(4). Experiments show that even if noise and clean speech parameters have Gaussian distribution (in log-domain), the corrupted speech parameters do not have Gaussian distribution anymore. However, if parameters have low variances, and in case a number of mixtures of Gaussians are used to model their distributions, the distribution of parameters can be still assumed to be Gaussian without much loss of accuracy and being able to use the same decoder optimized for Gaussian distribution.