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A Generalized Multidimensional Circulant Rational Covariance and Cepstral Extension Problem⁎This work was supported by the SID project "A Multidimensional and Multivariate Moment Problem Theory for Target Parameter Estimation in Automotive Radars" (ZORZ_SID19_01) funded by the Department of Information Engineering of the University of Padova. B. Zhu was also partially supported by the "Hundred-Talent Program" of the Sun Yat-sen University. Issue 7 (2021)
Record Type:
Journal Article
Title:
A Generalized Multidimensional Circulant Rational Covariance and Cepstral Extension Problem⁎This work was supported by the SID project "A Multidimensional and Multivariate Moment Problem Theory for Target Parameter Estimation in Automotive Radars" (ZORZ_SID19_01) funded by the Department of Information Engineering of the University of Padova. B. Zhu was also partially supported by the "Hundred-Talent Program" of the Sun Yat-sen University. Issue 7 (2021)
Main Title:
A Generalized Multidimensional Circulant Rational Covariance and Cepstral Extension Problem⁎This work was supported by the SID project "A Multidimensional and Multivariate Moment Problem Theory for Target Parameter Estimation in Automotive Radars" (ZORZ_SID19_01) funded by the Department of Information Engineering of the University of Padova. B. Zhu was also partially supported by the "Hundred-Talent Program" of the Sun Yat-sen University.
Abstract: We propose a general scenario to estimate the spectral density of an homogeneous random field from its moments. More precisely, we consider a multidimensional rational covariance and cepstral extension problem. The latter is usually solved by searching the spectral density maximizing the entropy rate while matching the moments. The generality of our mathematical formulation can be seen from the employed entropic index as well as the definition of cepstral coefficients. We characterize the solution in the circulant case. Finally, we apply our theory to a 2-d system identification problem.