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 Cramér-Rao bounds for threeand 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 threeor 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 also be valid for the uniform noise model of quantization.