The article studies parametric estimation of spectral moments of a zero-mean complex Gaussian stationary process immersed in independent Gaussian noise. With the merit of the maximum-likelihood (ML) approach as motivation, this work exploits a Whittle's (1953) type objective function that is able to capture the relevant features of the log-likelihood function while being much more manageable. The resulting estimates are strongly consistent and asymptotically efficient. As an example, application to Doppler weather radar data is considered.
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