Метод підвищення продуктивності корелограмного оцінювання спектральної густини потужності випадкових сигналів

Abstract

The method of increase of productivity of estimation of spectral density of power (SDP) of random signals at the expense of reduction of computational complexity of procedures of digital processing of investigated signals is offered in the work. The choice and substantiation of the methodology of digital evaluation of SDP signals is performed. It is proved that the correlogram methodology of SDP estimation under the condition of the same volume of processed signal samples is characterized by higher quality factor in comparison with direct estimation methods. At the same time, the application of the fast Fourier transform (FFT) technique to calculate the autocorrelation function of the signal creates conditions for improving the performance of correlogram methods for estimating SDP. Therefore, the correlogram methodology of fast digital estimation of SDP of random signals is applied in the work. A high-performance method for determining the autocorrelation function of the signal has been developed. In this paper, it is proposed to use the fast digital correlation theorem in order to accelerate the definition of the autocorrelation function. A recurrent relation is obtained to determine the discrete Fourier transform (DFT) of a subsequence in which a number of samples are updated. The proposed method requires two DFT and one reverse DFT. The synthesis of the correlation window function, which provides the maximum asymptotic rate of decline of the side lobes of the signal power spectrum for a given level of side lobes relative to the level of the main lobe of the spectrum. An expression for estimating the SDP of a random signal is obtained, according to which the statistical stability of the estimation is provided by averaging by processing segments, and correlation weighing allows to control the level of lateral parasitic petals of the spectrum of the studied signal. The research of productivity of the developed method of correlogram estimation of SDP of signals is executed. An expression is obtained to determine the coefficient of productivity, which takes into account the number of multiplication operations in the implementation of correlogram estimation of SDP. The results of the analysis proved that the proposed method makes it possible to significantly reduce the time for determining the SDP of random signals and to ensure the mode of operation of digital spectrum analyzers in a real time scale.