Evaluation of a Standardized Sine Wave Fit Algorithm

The IEEE Standard 1057 provides algorithms for fitting the parameters of a sine wave to noisy discrete time observations. The fit is obtained as an approximate minimizer of the sum of squared errors, i.e. the difference between observations and model output. The performance of the algorithm in x4.1.3.3 of the standard is compared both with the Cramér-Rao bound (CRB) on accuracy, and with the performance of a non-linear least squares approach. The algorithm of IEEE-STD-1057 provides accurate estimates in most practical applications for Gaussian and quantization noise. In the Gaussian scenario it provides estimates with performance close to the CRB. In severe conditions with noisy data covering only a fraction of a period, however, it has inferior performance compared with a one-dimensional search of a concentrated cost function.