COSH measure for speech processing

Abstract

Distance measures have been applied in such tasks as speaker verification, recognition, and variable frame rate transmission in vocoder systems. The DELCO algorithm, also known as the prediction residual or log likelihood ratio, has recently been applied in the abovementioned tasks. Although this procedure has been demonstrated to be of values in speech processing, (1) it does not satisfy from symmetry requirement for distance, i.e., the diatance from x to y is not equal to the distance from y to x, and (2) relationships between this measure and possibly more basic and physically meaningful measures, such as the root-mean-square (rms) difference between two log spectra, have not been shown. In this paper, the relationship between the likelihood measure and the rms measure is discussed and the nonsymmetrical property is illustrated. A cosh measure, related to two nonsymmetrical likelihood ratios, is then introduced with the following properties: (1) the symmetrical requirement for distance is satisfied, (2) its value, lying between the rms and peak value, can be related to log spectral differences, with large differences being weighted more significantly, (3) it equals the rms measure for small differences, and (4) it can be recursively evaluated using linear prediction techniques without FFT calculation. The nonuniform weighting property is believed to be of importance in speech processing since larger spectral differences generally occur near the formant frequencies.