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In the study of stationary processes on the real line, the spectral density function is a parameter of considerable interest.In this talk, we consider a new estimator of the spectral density function obtained by a regularized inversion of estimated covariances.In particular, the data are not required to be observed on a grid and the estimator is not based on the periodogram.For data that are observed on a grid, thc estimator is derived in closed from, and the mean squared error of the estimator can be computed.A numerical study is included to illustrate the methodology.The spectral density for an isotropic intrinsically stationary spatial process estimation will also be discussed.