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Spectrum at the output of DFT filter

Estimation of the energy spectrums of reflections in pulse Doppler weather radars. Part 2. Extreme performance

David I. Lekhovytskiy, Dmytro V. Atamanskiy, Dmytro S. Rachkov, Andrii V. Semeniaka


This is the second paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectra of random processes of different nature, which are determined by their samples at discrete moments of time. In this paper we analyze extreme performance of the reconstruction of continuous energy spectra, in particular, the ones of interperiod fluctuations of reflections from meteorological objects in pulse Doppler weather radars under the hypothetical conditions of a priori known covariance matrix of the analyzed processes. The reasons, which cause known disadvantages of classical (nonparametric) spectral estimation (SE) methods for energy spectrums shape reconstruction, are discussed. We have considered known and suggested criteria, using which the extreme performance of classical SE methods and parametric superresolution ones has been quantitatively compared. It has been demonstrated that the extreme performance of SE methods contains important but not comprehensive information. In order to choose a SE method appropriate for operation under real-world conditions, this information should be used together with information on a corresponding method’s adaptive performance under a priori unknown statistical characteristics of input effects.

In the article we used the acronyms, abbreviations and mathematical notations, which were presented in the first paper (see link [1]).


continuous energy spectrum of random processes; spectral function; spectral estimation methods; autoregressive model; meteorological object; Doppler weather radar; whitening filter

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