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Control Optim."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In the present paper we consider the problem of estimating the multidimensional power spectral density which describes a second-order stationary random field from a finite number of covariance and generalized cepstral coefficients. The latter can be framed as an optimization problem subject to multidimensional moment constraints, i.e., to search a spectral density maximizing an entropic index and matching the moments. In connection with systems and control, such a problem can also be posed as finding a multidimensional shaping filter (i.e., a linear time-invariant system) which can output a random field that has identical moments with the given data when fed with a white noise, a fundamental problem in system identification. In particular, we consider the case where the dimension of the random field is greater than two for which a satisfying theory is still missing. We propose a multidimensional moment problem which takes into account a generalized definition of the cepstral moments, together with a consistent definition of the entropy. We show that it is always possible to find a rational power spectral density matching exactly the covariances and approximately the generalized cepstral coefficients, from which a shaping filter can be constructed via spectral factorization. In plain words, our theory allows us to construct a well-posed spectral estimator for any finite dimension.<\/jats:p>","DOI":"10.1137\/21m1452937","type":"journal-article","created":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T05:50:45Z","timestamp":1686808245000},"page":"1532-1556","source":"Crossref","is-referenced-by-count":6,"title":["A Well-Posed Multidimensional Rational Covariance and Generalized Cepstral Extension Problem"],"prefix":"10.1137","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2297-0828","authenticated-orcid":true,"given":"Bin","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Gongchang Road 66, 518107 Shenzhen, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5581-5210","authenticated-orcid":true,"given":"Mattia","family":"Zorzi","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Padova, Via Gradenigo 6\/B, 35131 Padova, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/0326053"},{"key":"ref2","volume-title":"Multidimensional Systems Theory and Applications","author":"Bose N. 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