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Sequential analysis of signals in nonorthogonal basis


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

The article describes the serial analysis of signals, proposed by Kharkevich A.A. for the simplest model of spectral device containing one contour with variable frequency of adjustment and the unlimited set of contours with fixed mutually orthogonal of natural oscillations. There is shown the completeness of the nonorthogonal system of natural oscillations of all the paths aggregate in the article. Also, given the coefficients of the expansions formulas. Proved the convergence of the expansions. Provided the estimation of the rate of convergence of expansions. For a rectangular impulse there are graphed that illustrate the convergence rate. Noted Gibbs phenomenon, typical for the classical trigonometric orthonormal systems.Built the expansion of harmonic signal.


  1. Bari N.K. Trigonometricheskie rjady. M.: Gosudarstvennoe izdatelstvo fiziko-matematicheskojj literatury. 1961. 936 c.
  2. KHarkevich A.A. Spektry i analiz. M.: Librokom. 2009. 240 s.


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