1. A method of modifying HMM models trained on clean speech with cepstral mean normalization to provide models that compensate for simultaneous channel/microphone distortion and background noise (additive distortion) comprising the steps of: for each speech utterance calculating the mean mel-scaled cepstrum coefficients (MFCC) vector {circumflex over (b)} over the clean database; adding the mean MFCC vector {circumflex over (b)} to the mean vectors m p,j,k of the original HMM models where p is the index of PDF, j is the state, and k the mixing component to get in m p,j,k ; for a given speech utterance calculating an estimate of the background noise vector {tilde over (X)}; calculating the model mean vectors adapted to the noise {tilde over (X)} using m p,j,k &equals;IDFT (DFT ({overscore (m)} p,j,k ⊕DFT ({tilde over (X)})) to get the noise compensated mean vector where the Inverse Discrete Fourier Transform is taken sum of the Discrete Fourier Transform of the mean vectors {overscore (m)} p,j,k modified by the mean MFCC vector {circumflex over (b)} added to the Discrete Fourier Transform of the estimated noise {tilde over (X)}; and calculating the mean vector {circumflex over (b)} of the noisy data over the noisy speech space, and removing the mean vector {circumflex over (b)} of the noisy data from the model mean vectors adapted to noise to get the target model.