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A method is presented for parametric modeling of stationary random fields. The class of parametric models considered allows the most general elliptic field, and by linear constraints can include such special cases as isotropic, quarter plane, and separable fields. The technique, based on the cepstrum, has the great advantage of requiring only the use of fast Fourier transforms in the fitting process. Thus, unlike the fitting of two-dimensional autoregressions, no iteration is necessary. Other advantages are that any (Wiener) filters constructed from the fitted spectrum are guaranteed to be stable, and that the spectrum is guaranteed to be positive. Statistical tests for determining various special types of field from data are developed. The choice of model order is discussed as well.