L.S. Chudnovsky1, V.Yu. Krylov2

1,2 JSC “Precision Systems and Instruments” (Moscow, Russia)

Formulation of the problem. The problem of restoring the electromagnetic radiation of lightning discharges that have traveled long distances, including those with reflections from the ionosphere, to free space is relevant in geophysical monitoring systems.

Target. Restore the signal to free space from the zeros of the Fourier image with an accuracy of amplitude and arrival time, consider the problem of finding the delay time of the sum of the direct and delayed components for optical signals.

Results.  An extension of this method to more complex signals is proposed, using the example of receiving the diffraction and reflected components of low-frequency electromagnetic radiation. The method of zeros of the Fourier image allows solving inverse problems of signal recovery to free space based on the analysis of received radiation at different reception points with different path distortions. An example of separation of a direct optical pulse and a superimposed flare is considered, when the delay time is much shorter than the radiation duration. An example of reconstructing a point acoustic pulse from registration data with different filters (sets of different tubes) is analyzed.

Practical significance. Using the method in passive monitoring systems operating on the difference-range method of notching the coordinates of optical, acoustic and electromagnetic pulses to solve the problems of recognizing hypotheses.

Chudnovsky L.S., Krylov V.Yu. Separation of repeating signals by zero coordinates in the complex frequency plane. Radiotekhnika. 2023. V. 87. № 4. P. 113−122. DOI: https://doi.org/10.18127/j00338486-202304-14 (In Russian)

1. Oppengaim E. Chiphrovayu obrabotka rechevikh signalov. Primenenie chiphrovoyu obrabotki signalov. M.: Mir publishers. 1980.
   Р. 137-192 (In Russian).
2. Tihonov A.N., Arsenin V.Ja. Metody reshenija nekorrektnyh zadach. M.: Nauka. 1986 (In Russian).
3. Chudnovskij V.S., Chudnovskij L.S., Ageev V.M., Busygin V.P., Vagin Ju.P., Groznov I.V., Groznov A.V., Karhov A.N., Kolodochkin E.S., Mozgov K.S., Panov S.A., Puzanov Ju.V., Stal' N.L. Registracija izluchenij molnievyh razrjadov v raznostno-dal'nomernyh sistemah kosmicheskogo monitoringa. Jelektromagnitnye volny i jelektronnye sistemy. 2011. T. 16. № 3. S. 51-57 (In Russian).
4. Hurgin Ja.I., Jakovlev V.P. Finitnye funkcii v fizike i tehnike. M.: Nauka. 1971 (In Russian).
5. Ivanov V.V., Chernyj G.P. Metod vosstanovlenija signalov v istochnike, osnovannyj na interpretacii metoda priznakov. V kn.: Obratnye zadachi teorii rassejanija i teorii statisticheski-nereguljarnyh traktov. M.: ANSSSR. 1979. S. 108-141 (In Russian).
6. Ivanov V., Mihajlova T.E. Vosstanovlenie istochnika cunami 12 ijulja 1993 goda po sejsmicheskim dannym. Vulkanologija i sejsmo-logija. 1997 (In Russian).
7. Ivanov V.V. O razreshenii povtoryuuchikhsyu signalov. Impulsnie electromagnitnie polyu i izmerenie ikh parametrov. M.: Atomizda. 1976. S. 169-174 (In Russian).
8. Chudnovskiy L. Trace Distortion Correction. AIS-2014 «ATMOSPHERE, IONOSPHERE, SAFETY». Kaliningrad. 2014. P. 203-210.
9. Doluhanov M.P. Rasprostranenie radiovoln. M.: Svjaz'. 1965. 400 s. (In Russian).
10. Lin Y.T., Uman M.A., Standler R.B. Lightning Return Stroke Models. J. Geophys. Res. 1980. V. 85. № C3. P. 1571.
11. Fok V.A. Problemy difrakcii. M.: Sovetskoe radio. 1970. 520 s. (In Russian).
12. Chernyj F.B. Rasprostranenie radiovoln. M.: Sovetskoe radio. 1962. 479 s. (In Russian).
13. Markushevich A.I. Teoriyu analinicheskikh funkchiy. M-L.: GITTL. 1950. S. 703 (In Russian).
14. Ivanov V.V., Garder O.I. O vosstanovlenii istochnika po signalu slozhnoj formy. Voprosy radiojelektroniki. 1984. Vyp 8. Serija Jelektronnaja vychislitel'naja tehnika. S. 110-116 (In Russian).
15. Chudnovsky L.S., Minaev V.A., Chomyukov D.I. Analiz impylsa stirauchei golovki magnitofona pri otklutenii kanala zapisi. Mechdunsrodnayu konferenchiyu pravookhranitelniky system. M. 1995. S. 79-70 (In Russian).