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Ageev D.V. model of harmonic signal selection


S.V. Shibirin – Ph. D. (Eng.), Senior Research Scientist, JSC «Russian Space Systems» (Moscow) E-mail:

This article examines the linear selection of harmonic signals model proposed by Ageev D.V. in 1935. For systems described by linear functional, the initial task reduces to construction of biorthogonal systems for the given system of instrument function. The article proves the incorrectness of solving the problem in the signal space L2[−1;+1] for any finite set of systems. There are given sufficient conditions for the uniqueness of solution. The solutions of non-orthogonal instrument functions and their spectral properties are given. The problem of radio-channel frequency-division is considered. It’s showed that the possibility of solving this problem exists for any finite number of harmonic signals is given frequency range.


  1. Ageev D.V. Osnovy teorii linejjnojj selekcii // Nauchno-tekhnicheskijj sbornik svjazi LEHIS. 1935. № 10. S. 8−28.
  2. Viner N., Pehli R. Preobrazovanie Fure v kompleksnojj oblasti. M.: Nauka. 1964. 268 s.
  3. Levin B.JA. Raspredelenie kornejj celykh funkcijj. M.: GITTL. 1956. 632 s.
  4. Riesz F. Sur les ensembles de founctions // Comptes rendus. 1906. P. 738−741.


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