A family of distortion measures based upon projection operation for robust speech recognition

Consideration is given to the formulation of speech similarity measures, a fundamental component in recognizer designs, that are robust to the change of ambient conditions. The authors focus on the speech cepstrum derived from linear prediction coefficients (the LPC cepstrum). By using some common models for noisy speech, they show analytically that additive white noise reduces the norm (length) of the LPC cepstral vectors. Empirical observations on the parameter histograms not only confirm the analytical results through the use of noise models but further reveal that at a given (global) signal-to-noise ratio (SNR), the norm reduction on cepstral vectors with larger norms is generally less than on vectors with smaller norms, and that lower order coefficients are more affected than higher order terms. In addition, it is found that the orientation (or direction) of the cepstral vector is less susceptible to noise perturbation than the vector norm. As a consequence of the above results, a family of distortion measures based on the projection between two cepstral vectors is proposed. The new measures have the same computational efficiency as the band-pass cepstral distortion measure