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Method for Comparison Testing of Parametric Power Spectrum Estimates: Spectral Analysis Via Time Series Synthesis

  • ACOUSTIC MEASUREMENTS
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Measurement Techniques Aims and scope

The task of comparison testing of time series power spectrum parametric estimates is considered. It is shown that an urgent problem that arises in solving it is the optimization of the parameters of spectral estimates under conditions of small samples of observations. To overcome this problem, it is proposed to use the system-wide concept of analysis through time series synthesis. Based on this concept, a regular method was developed for comparison testing of parametric estimates of the power spectrum that are obtained from a time series of finite duration. Within the method, solutions are accepted based on the results of testing statistical hypotheses about the homogeneity of two samples: the finite empirical one, compiled based on the results of observations, and an infinite virtual one, mathematically synthesized according to each individual parametric estimate in the series of spectral alternatives being examined. The principle of minimum informational divergence between samples according to the Kullback–Leibler criterion. An example of the practical application of the developed method is presented in the problem of discrete spectral modeling of speech signals. The ability of the method to identify patterns of unstable parametric estimates of the autoregressive type has been shown. The results obtained are intended for use in the field of speech acoustics, as well as technical and medical diagnostics, where parametric methods of spectral analysis are increasingly used in practice.

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Notes

  1. QATestlab (site) URL:https://blog.qatestlab.com/2012/10/01/types-of-software-testing-comparison-testing/. (Date accessed May 17, 2023).

  2. Since moments no greater than second order are used in spectral analysis of a random process, the assumption regarding the Gaussian distribution law of sample Xr does not limit in any manner the generality of the study performed later.

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  1. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    V. V. Savchenko

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Translated from Izmeritel'naya Tekhnika, No. 6, pp. 56–62, June, 2023. https://doi.org/10.32446/0368-1025it.2023-6-56-62.

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Savchenko, V.V. Method for Comparison Testing of Parametric Power Spectrum Estimates: Spectral Analysis Via Time Series Synthesis. Meas Tech 66, 430–438 (2023). https://doi.org/10.1007/s11018-023-02244-3

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