Distortion measures for speech processing

Several properties, interrelations, and interpretations are developed for various speech spectral distortion measures. The principle results are 1) the development of notions of relative strength and equivalence of the various distortion measures both in a mathematical sense corresponding to subjective equivalence and in a coding sense when used in minimum distortion or nearest neighbor speech processing systems; 2) the demonstration that the Itakura-Saito and related distortion measures possess a property similar to the triangle inequality when used in nearest neighbor systems such as quantization and cluster analysis; and 3) that the Itakura-Saito and normalized model distortion measures yield efficient computation algorithms for generalized centroids or minimum distortion points of groups or clusters of speech frames, an important computation in both classical cluster analysis techniques and in algorithms for optimal quantizer design. We also argue that the Itakura-Saito and related distortions are well-suited computationally, mathematically, and intuitively for such applications.