We propose an algorithm for estimating the parameters of a signal from its quasiharmonic representation and a method for estimation of slowly varying coefficients of a second-order differential equation. The considered approach uses Tikhonov’s regularization for the class of slowly varying functions. The results of statistical modeling for the Mathieu equation are presented. Solution of the frequency comparison problem on the example of estimation of the frequency instability of a quartz resonator setting a signal sampling rate is considered. Relations for determining the sampling rate are obtained and the results of numerical simulation are reported.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 53, No. 2, pp. 145–159, February 2010.
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Ignatjev, V.K., Nikitin, A.V. & Yushanov, S.V. Parametric analysis of oscillations with slowly varying frequency. Radiophys Quantum El 53, 132–145 (2010). https://doi.org/10.1007/s11141-010-9209-9
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DOI: https://doi.org/10.1007/s11141-010-9209-9