A large class of signals can be conveniently modeled by a stationary first-order Markoff process. This paper shows that for such a process the elements of the covariance matrix in the discrete Fourier transform domain can be calculated in closed form which facilitates a direct comparison of the transform with the discrete Karhunen-Loéve transform of KLT. A similar technique is applied to the analysis of the discrete consine transform or DCT. Both transforms are shown to be asymptotically equivalent to the KLT, i.e., they become equivalent to it as the block size or the number of sample points approaches infinity. Significant conclusions in this paper are that in the DCT domain the residual correlation is surprisingly smaller than in the DFT domain even for a nominal block size and that the decorrelation by the DCT is relatively immune to statistics change.

In order to evaluate the speaker-factor in uttered words, multivariate analysis of variance for four-factor design with repeated measurements has been applied to the analysis of the spectral vectors obtained from Japanese V₁ CV₂ utterances by 10 adult male speakers, where V₁, V₂/a, i, u, e, o/ and Cm, n, η/. The speaker, the vowel V₁, the consonant C, and the vowel V₂ have been assigned to the four factors, respectively, and the interaction between speaker-factor and V₁, C or V₂-factor has been especially interesting in the analysis. As the results, what we should take into account as to the co-articulation of a certain phoneme are (1) the main effect of the phoneme, (2) the main effect of the just preceding (or following) phoneme, (3) the interaction between the phoneme and the just preceding (or following) phoneme, and (4) the main effect of the speaker-factor. The interactions between the speaker-factor and these phonemes are relatively small, and the influence of the speaker-factor to the co-articulation is not so complicated. These facts imply possibility of the speaker-independent description about the phoneme and the rule of co-articulation.

This paper presents a method of extraction of the requested information from English sentences which express a certain fact or relations. The restricted input-English sentences are deterministically reduced using the context-free-type production rules presented here, which is constructed tentatively by introducing nonterminal symbol with subscript-variables. And the corresponding logical expressions are constructed. Extractions of requested informations are efficiently performed using the transformation rules between atomic and functional expressions.