Модификация метода Тьюки – Хеннинга оценки спектральной плотности с помощью рекурсивного вычислительного алгоритма в схеме адаптивной фильтрации
Authors: Фадеева Л.Ю. , Папазян С.Г. 
Published: February 2025

Предлагается рекурсивный вычислительный алгоритм в схеме адаптивной фильтрации, интеграция в который модифицированного метода Тьюки – Хеннинга позволит повысить разрешение оценки спектральной плотности и кардинально изменить результат этой оценки. В основе разработанного авторами алгоритма лежит известный метод прикладной математики – метод деления отрезка пополам, в соответствии с которым диапазон измерений спектральной плотности сужается к окрестностям её пиков.

Introduction. With the advent of modern information processing systems, when signal processing needs to be carried out in real time, research and development in the field of adaptive signal filtering continue to keep relevance. Current tasks include correction and suppression of echo signals, multipath propagation in high frequency systems, speech processing, digital communication systems, wideband networks and systems where multipath effects are observed. In particular, it was previously shown that the problem of reducing the influence of additive interferences can be solved by adaptation in the frequency domain by applying the procedure of spectral processing of input and reference signals and estimating their spectral density. This processing reduces the influence of additive interferences on the resulting estimate and increases the efficiency of the system. Real devices often have their own uncorrelated additive wideband Gaussian noise, which significantly reduces the efficiency of the adaptation algorithm and the operation of the entire filtering system. However, the unification of various methods in the conditions of the posed tasks is still topical. Objective. The aim of this work is to increase the efficiency of the adaptive correction filter using the computational algorithm developed by the authors, which is a modification of the Tukey –Henning method for estimating spectral density, the embedding of which in the recursive algorithm leads not only to the detection of its new peaks and to their other quantitative estimation, but also to a reduction in the influence of adaptive noise, which positively affects the quality of filtering the useful signal. The key approach to solving the problems related to spectral density estimation is the Wiener-Khinchin formula. The Tukey-Hanning method modernized in this research is a modification of the Blackman-Tukey method, which in turn is based on a modification of the Wiener-Khinchin formula. The authors added (integrated) a computational algorithm into the modification of the Tukey-Hanning method, which allowed not only to improve the accuracy of the spectral density estimate, but also to radically change it. This algorithm is based on the method of dividing the segment in half, according to which the measurement range is narrowed to the vicinity of the peaks of the spectral density. In this case, the sequence of numbers m, which determines the frequency measurement step, is set randomly. Methodology and findings of the experiment. The proposed algorithm was studied in relation to a random signal, the model of which is the sum of two harmonic oscillations with the same amplitudes and initial phases, which differ in frequency values close to each other. The experiment was carried out using simulation in the LabVIEW framework. With the use of the signal model in LabVIEW, the autocorrelation function of the studied signal was restored according to autocorrelation estimates. The described iterative procedure is considered on the example of the analyzed signal. Estimates of the power spectral density are obtained using the proposed computational algorithm. It was shown that the obtained estimates are more accurate compared to the classical Tukey–Henning algorithm: they reflect the power level of the spectral components of the useful signal as objectively as possible; they have low sensitivity of their values to the influence of additive white Gaussian noise. Conclusions. The discussed features of the modified Tukey–Henning method allow us to conclude that its use in the adaptive filtering scheme in the frequency domain is a reasonable measure that positively affects the filtering quality of the useful signal. The application of the Tukey–Henning method together with the computational algorithm proposed by the authors seems promising in other radio engineering applications, for example, in problems of spectral estimation of methods and purity of surface treatment in the development of various kinds of high-precision sensors, film and semiconductor submicron and nanoscale microelectronics elements, as well as in predicting their physical and electrical properties.