Matrix calculation of correlation characteristics based on spectral methods

Abstract

The paper is devoted to the problem of calculation of autocorrelation function that is important for solving the tasks that require finding the repeating intervals of the signal or defining the main frequency of the signal against the background of non-stationary noise. The authors propose an algorithm to transform the connection between arithmetic and logical correlation functions in oriented basis into the matrix form. Comparative analysis is conducted for the computational complexity of different types of autocorrelation functions using different spectral methods — Fourier, Walsh, and oriented basis transform.