Development of a Digital Model of a Beta Function Based on Mellin’s Integral Transforms

Abstract

The implementation of a digital model of the beta function for use in computer algorithms is a time-consuming task. This is due to the complexity of the high-precision representation of its integrand functions, which require a large number of intermediate operations, which entails a large load on the computational power. Purpose: Development of the basic theoretical provisions of the integral Mellin transform in relation to the theory of signal processing against the background of noise and research of their discrete representation. Results: It is shown in the paper that the beta function can be considered as a special case of Mellin’s integral transforms. Based on this statement, a mathematical model of the beta function was developed. Using the properties of parametrically periodic oscillations belonging to the class of trigonometric-logarithmic functions, it was possible to create a digital model for representing the beta function. Practical relevance: Based on the established digital model can be realized a high-speed algorithm for calculating the beta function with a given accuracy. Such algorithms can serve as a basis for creating signal processing programs in order to detect wideband phase-shift keyed signals against a background of noise with an unknown phase sequence. An example of using such algorithms is the search for Wi-Fi bugs.