International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Partial differential equations (PDEs) are differential equations in which there is more than one independent variable. They arise in the modelling of a wide-range of physical phenomena including electromagnetism, fluid flow, elasticity, quantum mechanics and heat conduction. The wave equation serves as a fundamental model for understanding various wave phenomena in physics and engineering. In this paper, we explore the application of Sturm-Liouville problems to solve the wave equation. The results of our investigations not only showcase the accuracy and computational advantages of the Sturm-Liouville method but also shed light on the physical interpretations of the obtained eigenfunctions and eigenvalues. In conclusion, this paper contributes to the body of knowledge regarding the application of SturmLiouville problems in wave equation modeling and analysis. It offers a valuable perspective for researchers, scientists, and engineers seeking efficient and insightful solutions to wave-related challenges. The versatility and effectiveness of the Sturm-Liouville approach make it a compelling tool for gaining deeper insights into wave phenomena and their practical applications.

In this paper we will study an important part of the speech signal processing, the reconstruction of the signal. We will use the Newton interpolation method with a deterministic model and warped frequencies in order, maybe, to get a better reconstruction process of the signal. To determine the efficiency of the method we will use two criteria like: accuracy of reconstruction, noise stability. Then we will test this algorithm using the criteria that we proposed above versus the classic Yen’s algorithm. At the end of our experiment we will see that in noise stability our algorithm performs better but not in the reconstruction accuracy. In overall Yen’s algorithm performs slightly better.