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The problem of estimating continuous-domain autoregressive moving-average processes from sampled data is considered. The proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes. We derive an exact evaluation of the discrete-domain power-spectrum using exponential B-splines and further suggest an estimation approach that is based on digitally filtering the available data. The proposed functional, which is related to Whittle's likelihood function, exhibits several local minima that originate from aliasing. The global minimum, however, corresponds to a maximum-likelihood estimator, regardless of the sampling step. Experimental results indicate that the proposed approach closely follows the Cramér-Rao bound for various aliasing configurations.