Dimensional Analysis and Display of Speech Spectra

Abstract

Real-time spectrographic analysis involves processing of spectral outputs as vectors in multidimensional space. To reduce the number of dimensions and eliminate redundancy between channels, a covariance matrix can be derived and the eigenvectors calculated. Correlating the spectral cross sections with as few as three eigenvectors can account for up to 98% of the total variance. Following the theory of Yilmas [H. Yilmas, NASA Contract 12–129, Final Rept. (Dec. 1966)], a real-time display using correlations of the first three eigenvectors has been written for a PDP-1 computer. The display consists of a circle representing a cross section of a cone, and a vector representing cone height. The height represents loudness, as determined by the correlation of the first eigenvector; and the circle is analogous to a vowel circle derived from Eigenvectors 2 and 3, normalized for volume by Eigenvector 1. The display provides effective phoneme separation: display coordinates are useful for automatic phoneme identification. The eigenvectors can be quickly recalculated to accommodate variations in language or speech type.

Principal-components analysis for low-redundancy encoding of speech spectra

“…The procedure as just outlined insures that, for a given number of principal components, the average mean-square error between the original and reconstituted data is minimized. Kramer and Mathews (1956), as well as Kulya (1964) and Boehm and Wright (1968), formulated the data-reduction procedure in a somewhat different manner than just described, in that the constant value terms indicated in the right-hand box of Fig. i were not allowed..…”