An acoustical model demonstrating the effect of additive noise and channel filtering over a clean speech signal is shown in Figure 1.

The corrupted speech is given by:

where is sample number. In power spectral domain:

where , , and represent log-spectral energies of clean signal, additive noise, convolutive noise and corrupted signal respectively, for given frequency .

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.