Acoustical properties of speech have been shown to be related to mental states such as remission and depression. The objective of this project was to relate the energy in frequency bands with the severity of the mental state using the Beck Depression Inventory (BDI). Recorded speech was obtained from male and female subjects with mental states of remission, depression, and suicidal risk. These subjects had recorded automated and spontaneous speech samples. Multiple regression analysis was used to relate the independent energy band ratio variables with the dependent BDI scores, and thus allow the determination of equitable BDI scores for future patients. For the male group, the square of the 3rd energy band and the cross-product of the 2nd and 3rd energy band were prominent in both the reading and interviewed groups. Therefore the equation with the 2nd lowest Akaike Information Criterion (AIC) score was chosen for the reading male group, and the 1st lowest AIC score was chosen for the interviewed male group. For the female group, the square and cross-product of the 1st and 2nd energy bands were prominent in both the reading and interviewed groups. Therefore the 2nd lowest AIC score was chosen for the reading female group, and the 1st lowest AIC score was chosen for the interviewed female group. The clinician could thus determine the patient’s mood or state of mind by comparing the estimated BDI score with the ranges of total BDI scores: remitted 0 – 20, depressed 15 – 38, suicidal 38 – 46.
Keywords: speech, mental states, power spectra, multiple regression, information theoretic criterion
Quantum differentials on cross product Hopf algebras