DETERMINATION OF THE COEFFICIENTS OF A RATIONAL ANALYZING FUNCTION USING THE METHOD OF LEAST SQUARES

Abstract

Background. This research relates to the field of aircraft location using electrostatic reconnaissance equipment. For digital processing of non-stationary electrostatic sensor signals of the system in question, convolution from the analyzing function, including a special type for a specific signal, is usually used. In this paper, a new algorithm for the synthesis of the analyzing function is proposed. Materials and methods. The least squares method was used as the initial synthesis method. The equations describe the target properties of a rational analyzing function. The properties are selected in accordance with the algorithm of using the modified Morlet wavelet function. In addition, the analyzing function was chosen to be similar to the one being analyzed. When writing the properties of functions in the form of equations, the integrals were revealed through Cauchy's residue theorem. Results. An algorithm is described and implemented that determines the coefficients of the analyzing function programmatically. Conclusions. The presented algorithm determines the coefficients of the analyzing function more accurately and in much less machine time than the algorithm based on gradient search.

Keywords

• electrostatic signal
• electrostatic monitoring
• electrostatic location
• digital signal processing
• time-frequency distribution