Upper and lower bounds on the mean of noisy speech: Application to minimax classification

In this paper, we derive upper and lower bounds on the mean of speech corrupted by additive noise. The bounds are derived in the log spectral domain. Also approximate bounds on the first and second order time derivatives are developed. It is also shown how to transform these bounds to the Mel frequency cepstral coefficient (MFCC) domain. The proposed bounds are used to define the mismatch neighborhood for minimax classification. It is shown that this parametric neighborhood works quite well for artificially added noise and for a real-life mismatch scenario (moving car environment) which does not fully conform with the theoretical conditions used to derive the bounds. In contrast to traditional neighborhood structure for minimax classification, no empirical tuning of the bounds is required. It is believed that the applicability of the derived bounds is not limited to a minimax setting and can be potentially used to develop various compensation scenarios in the log spectral domain.