About the Recognition and Reconstruction Two Unknown Functions From Known Their Tandem

Vladimir V. Arabadzhi

Paper is devoted to the area of processing of physical signals and data or artificial perception. The incoming data are presented in the form of defined sum of two unknown functions, spaced on finite carrier. Practical examples of the functions searched for can be presented: (a) by very closely spaced two atomic spectrums of radiation; (b) by the output signal of some telescope, scanning two point-like sources with angle distance between each other much less, than the angle width of main petal of telescope's directivity pattern. So the presented result can be classified as some case of the known problem of superresolution. It is shown, that two functions of tandem (mutually overlapping each other) can be reconstructed separately by using only three it is correct chosen numbers. The class of functions (and their tandems), which are overlapping each other and allows single reconstruction of both searched functions and also conditions of the correctness of the decision are formulated. The method of separation of two functions had been tested numerically on the variety of typical practical examples. The stability of suggested numerical procedure is confirmed in the presence of uncorrelated errors of measurements and calculations at each point of tandem.