IEEE Standard 1057, Crame´r-Rao bound and the parsimony principle

This paper deals with some fundamental properties of the sine-wave-fit algorithm included in IEEE Standards 1057 and 1241. Asymptotic Crame´r-Rao bounds (CRBs) for three and four model parameters are derived under the Gaussian assumption. Further, the sine-wave-fitting properties of the algorithm are analyzed by the parsimony principle. A decision criterion whether to use the three- or four-parameter model is derived. It is shown that a three-parameter sine-wave fit produces a better fit than the four-parameter fit if the frequency is known to be within an interval related to the number of samples and the signal-to-noise ratio. By a numerical analysis, the theoretical results are shown to be also valid for the uniform noise model of quantization.