Biharmonic Equations Integrals Application Features at Signals Restoration by Means of Interpolation Polynomials
Andriy Makarchuk, Inna V. Kal’chuk, Yu. I. Kharkevych, Svіtlana Salnikova · 2021
Most of the real signals are continuous functions. To process such signals, we must converted them into digital form, and vice versa reproduce the corresponding analog prototype by a set of individual signals streams. Today the number of mathematical techniques for constructing a continuous signal representation using its discrete representation have been developed and studied in the works of many researchers. The discrete Fourier transformation is well-known tool of this kind. In addition, many other methods of such signal restoration have been studied. In practice, interpolation is used for this purpose. Interpolation polynomials based on integrals have quite good approximate properties. The paper presents the new method for constructing interpolation polynomials and illustrates the qualitative improvement in signal reproduction using interpolation polynomials based on the Abel-Poisson integral and the biharmonic integral.