Algorithms for Evaluation of Polynomial Models of Digital Signal by the Weighted Least Squares Method for Solving Problems Process Control

Abstract

Nowadays, signal modeling and processing plays an important role in information management systems for various purposes, including those oriented to monitoring and controlling technological processes. This is due to the fact that the effectiveness of these systems is determined by the quality of the information used to solve the functional tasks assigned to them. The information's quality improving is inextricably linked with the use of digital signal processing methods and algorithms for processing measurement information.Discrete transformations are effectively used to solve a wide range of digital signal processing tasks. These transformations are a recognized tool for creating computationally efficient algorithms for solving digital signal processing problems. The study proposes algorithms for estimating polynomial models of digital signals by the weighted least-squares method based on transformations in discrete bases of oblique Walsh functions. The analysis of the computational complexity of the developed algorithms using the vector criterion is carried out. The computational complexity of the proposed estimation algorithms is reduced in comparison with the direct algorithm and the spectral algorithm based on discrete Walsh transforms. The advantage of the proposed algorithms is the low multiplicative complexity and their focus on efficient implementation using binary arithmetic.