Cramér–Rao Lower Bound for Unbiased Estimators of Sampled Noisy Sine-Wave Parameters

In this article, the Cramér–Rao lower bounds (CRLBs) for unbiased estimators of sampled real-valued sine-wave parameters are analyzed. Sine-wave frequency is assumed either known or unknown, and both coherent and noncoherent sampling conditions are considered. It is shown that the CRLBs coincide with the relationships widely used in the literature only when both coherent sampling occurs and the sine-wave frequency is known. In fact, when few sine-wave cycles are observed, errors associated with the widely used relationships may be significant. Approximate, but accurate and quite simple expressions for the CRLBs are also proposed in this article. All the derived expressions are verified through numerical results or computer simulations.