МЕТОД ДОСЛІДЖЕННЯ МАТЕМАТИЧНОЇ МОДЕЛІ ЗСУНУТОГО ЧАСУ ДВОФРАГМЕНТНОГО СИГНАЛУ З НЕЛІНІЙНОЮ ЧАСТОТНОЮ МОДУЛЯЦІЄЮ

Context. The further development of the theory and techniques for forming and processing complex radar signals encompasses both the study of existing mathematical models of probing radio signals and the creation of new ones. One of the directions of such research focuses on reducing the maximum side lobe level in the autocorrelation functions of signals with intra-pulse modulation of frequency or phase. In this context, the instantaneous frequency may vary according to either a linear or nonlinear law. Nonlinear frequency modulation laws can reduce the maximum level of side lobes without introducing amplitude modulation in the output signal of the radio transmitting device and, consequently, without causing power loss in the sensing signals. The widespread implementation of nonlinear-frequency-modulated signals in radar technology is constrained by the insufficient development of their mathematical models. Therefore, the development of methods for analyzing existing mathematical models of signals with nonlinear frequency modulation remains an urgent scientific task.Objective. The purpose of this work is to develop a method for conducting research to evaluate the advantages and disadvantages of a mathematical model of a nonlinear-frequency-modulated signal consisting of two fragments with linear frequency modulation.Method. This study proposes a method for analyzing mathematical models of signals based on the transition from a shifted time scale to the current time scale. The methodology consists of the following main stages: a formalized description of mathematical models, transition to an alternative time scale, identification of components and determination of their physical essence, and a comparative analysis. The proposed method was validated through simulation modeling.Results. Using the proposed method, it has been determined that the mathematical operation of time scale shifting is equivalent to the introduction of additional components in the mathematical model. These components simultaneously and automatically compensate for the frequency jump at the junction of fragments, as well as introduce an additional linear phase increment in the second linearly frequency-modulated fragment. This approach provides a clear illustration of the frequency jump compensation mechanism in the studied mathematical model. The applied method enabled the identification of a drawback in the examined mathematical model, namely, the absence of a compensatory component for the instantaneous phase jump during the transition from the first LFM fragment to the second.Conclusions. A method has been developed to determine the essence and corresponding influence of the components of amathematical model in a time-shifted, nonlinear, frequency-modulated signal, which consists of two fragments with linear frequency modulation. The model under study is not entirely accurate, as it lacks a component to compensate for the phase jump at the transition from the first signal fragment to the second. The introduction of such a component ensures a further reduction in the maximum level of the side lobes of the signal autocorrelation function.