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Calculation of the Harmonic Discrete Spectrums Short Signals


V.A. Toboev, M.S. Tolstov

Authors view a problem of calculation of discrete spectrums of short signals on the basis of a method of non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS), allowing to find optimum fitted function at a minimum quantity of harmonics which unequivocally determine an information-significant frequency band. The basic expedients of approximation of signals are viewed by a terminating trigonometric series and the algorithm of calculation of spectrums, suitable for practical embodying a new method is offered. Unlike the spectrums counted with use of integrals and a Fourier series, the new spectrum is not the predetermined set of harmonics, and depends on a concrete view of a signal. By way of the problem put in given operation most close to offered method NAFASS is method Prony which also allows finding spectrums of signals of the restricted duration. However it is under fulfilled with reference to the continuous signals and the area of its application is essentially restricted. For an illustration of opportunities of calculation of discrete spectrums by means of NAFASS three signals are analyzed as examples: an acyclic signal (multinomial’s Chebisev), a periodic signal from a casual component and monthly values of the Zurich numbers of Volf (a series of solar activity). The algorithm of representation of the restricted signal offered in operation can be used by terminating number of harmonics for a filtration and transformation of signals to systems of reception, the analysis and transfer of the information; interpolations and extrapolations of oscillatory and aperiodic processes of a various origin; detection and educations of the useful signal from зашумленных given, etc.

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