Keith Y. Patarroyo

Keith Y. Patarroyo

We propose boundary conditions for the diffusion equation that maintain the initial mean and the total mass of a discrete data sample in the density estimation process. A complete study of this framework with numerical experiments using the finite element method is presented for the one dimensional diffusion equation, some possible applications of this results are presented as well. We also comment on a similar methodology for the two-dimensional diffusion equation for future applications in two-dimensional domains.

Keith Y. Patarroyo, Vladimir Vargas-Calderón

The Vocal Joystick Vowel Corpus, by Washington University, was used to study monophthongs pronounced by native English speakers. The objective of this study was to quantitatively measure the extent at which speech recognition methods can distinguish between similar sounding vowels. In particular, the phonemes /\textipa{@}/, /æ/, /\textipa{A}:/ and /\textipa{2}/ were analysed. 748 sound files from the corpus were used and subjected to Linear Predictive Coding (LPC) to compute their formants, and to Mel Frequency Cepstral Coefficients (MFCC) algorithm, to compute the cepstral coefficients. A Decision Tree Classifier was used to build a predictive model that learnt the patterns of the two first formants measured in the data set, as well as the patterns of the 13 cepstral coefficients. An accuracy of 70\% was achieved using formants for the mentioned phonemes. For the MFCC analysis an accuracy of 52 \% was achieved and an accuracy of 71\% when /\textipa{@}/ was ignored. The results obtained show that the studied algorithms are far from mimicking the ability of distinguishing subtle differences in sounds like human hearing does.