Analysis of sounding signals of radioacoustic sounding systems of the atmosphere in the functional space

Systems of radio acoustic sounding (RAS) of the atmosphere provide information on the state of processes occurring in the lower layers of the atmosphere. They allow measuring vertical profiles of atmospheric temperature, wind speed, and air humidity. The obtained information is used in applied tasks to ensure the takeoff and landing of aircraft, weather forecasting, and the study of atmospheric processes. However, the effectiveness of the existing radio-acoustic means is insufficient, and there are practical needs for the development of appropriate promising structures and algorithms that will be implemented during the construction of specific stations. The article presents new approaches and a new mathematical apparatus developed for use in the analysis and synthesis of probing signals of the RAS systems. The process of interaction of acoustic and electromagnetic signals in the environment is described using functional analysis and abstract mathematical spaces, which will make it possible to consider such signals together, use visual geometric representations, and generally increase the effectiveness of the tasks of research and synthesis of such complex, heterogeneous signals. The features of the distance surfaces for different pairs of probing signals were studied using the method of mathematical modeling. The general regularities of the studied surfaces of signal distances are as follows: there is a certain main lobe of the surface in which the connection of sounding acoustic and electromagnetic signals of different physical nature is significant. As the values ​​of the parameters of the functional space increase, the degree of signal communication decreases, and depending on the shape of the contour signals, side lobes of the surface can be observed, the sizes of which depend on the characteristic features of the contours. The obtained research results will provide the possibility of setting up and solving the actual problems of analysis and synthesis of sounding signals using the mathematical apparatus of functional analysis.