In this paper, a new feature extraction method is presented based on spectro-temporal representation of speech signal for phoneme classification. In the proposed method, an artificial neural network approach is used to cluster spectro-temporal domain. Self-organizing map artificial neural network (SOM) was applied to clustering of features space. Scale, rate and frequency were used as spatial information of each point and the magnitude component was used as similarity attribute in clustering algorithm. Three mechanisms were considered to select attributes in spectro-temporal features space. Spatial information of clusters, the magnitude component of samples in spectro-temporal domain and the average of the amplitude components of each cluster points were considered as secondary features. The proposed features vectors were used for phonemes classification. The results demonstrate that a significant improvement is obtained in classification rate of different sets of phonemes in comparison to previous clustering-based methods. The obtained results of new features indicate the system error is compensated in all vowels and consonants subsets in compare to weighted K-means clustering.

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In this manuscript, we investigate the approximate solutions to the tangent nonlinear packaging equation in the context of fractional calculus. It is an important equation because shock and vibrations are unavoidable circumstances for the packaged goods during transport from production plants to the consumer. We consider the fractal fractional Caputo operator and Atangana–Baleanu fractal fractional operator with nonsingular kernel to obtain the numerical consequences. Both fractal fractional techniques are equally good, but the Atangana–Baleanu Caputo method has an edge over Caputo method. For illustrations and clarity of our main results, we provided the numerical simulations of the approximate solutions and their physical interpretations. This paper contributes to the new applications of fractional calculus in packaging systems.

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