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, the filter-bank energies is given as:

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

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 the same decoder optimized for Gaussian distribution can be used.