ESTIMATION OF SOFTWARE COMPLEXITY OF CALCULATION OF AUTOREGRESSION COEFFICIENTS AT DIGITAL SPECTRAL ANALYSIS

Abstract

The subject of research in the article are algorithms for fast calculation of autoregression coefficients in digital spectral analysis and estimation of the number of arithmetic operations required for their implementation. The aim of the article – comparative analysis of the speed of different algorithms for calculating the coefficients of autoregression as part of the algorithms of spectral analysis, including analysis of the complexity of their microcontroller implementation. Tasks to be solved: selection of spectral analysis methods suitable for diagnostics of technological equipment, analysis of methods for calculating autoregression coefficients and derivation of relations for estimating software complexity of algorithms and calculation of numerical estimates of addition and multiplication for some algorithms, adaptation of developed methods and estimates to microcontrollers. spectrum Applied methods: algorithm theory, Fourier transform, natural series, microcontroller programming. The results obtained: it is shown that spectral estimation methods based on Yul-Walker equations, which require the calculation of autoaggression coefficients, combine sufficient resolution and resistance to interference with acceptable implementation complexity. Estimates of the number of additions and multiplications for the Levinson, Durbin, and Trench algorithms are obtained, and their comparative analysis is performed. The calculation times for microcontroller arithmetic with fixed and floating points were count upon. Conclusions: When constructing spectrum analyzers for the diagnosis of technological equipment, it is advisable to use the Yul-Walker method. A comparison of Levinson, Durbin, and Trench algorithms for calculating autoregression coefficients showed that the Trench method requires a minimum number of additions, and the Durbin method requires a minimum number of multiplications. At microcontroller realization of spectrum analyzers, it is necessary to consider features of the arithmetic used by the controller. The Trench method is the fastest in the case of floating-point arithmetic and small-scale modeling. In other cases, Durbin's method is more effective.

Keywords

• spectral analysis;
• autoregression;
• Levinson;
• Durbin;
• Trench algorithms;
• computational complexity;