Weighted LS estimation of spectral contents and periodicity of signals comprising multi-frequency components

The goal of this paper is to apply the Weighted Least Squares method to accurately estimate the period and spectral contents of a noisy periodic signal that has many frequency components. The signal data record has a total number of periods that is not necessarily an integer, but is greater than two. There is no need for synchronization between the generator and the data acquisition, where the sampling rates may be different and the number of samples per period may not necessarily be an integer number. The estimation method is invoked by computing the noise variance first from an initial least squares estimate, which is then used for weighting the cost function of the Weighted Least Squares Estimator. It is shown that the accuracy of the estimated results is superior to estimates that are devoid of variance weighting, such as those engendered by the Least Squares Estimator.