A generalized multidimensional circulant rational covariance and cepstral extension problem

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.