Estimation of the period and spectral content of multi-frequency signals using minimal data without user interaction

Least Squares (LS) and Weighted Least Squares (WLS) cost functions are applied to estimate the period and spectral content of a periodic signal comprising many frequency components. The signal data record is more than two periods, and there is no user interaction. 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 be an integer number. An initial LS estimate of the signal spectrum is used to obtain an initial sample variance of the noise for weighting an initial WLS estimator. Using a sliding frequency domain window, a smooth sample variance of the noise is estimated from the signal spectrum. The smooth sample variance is then used as a weight in a second WLS estimator, different from the initial WLS estimator. It is shown that the estimate of the second WLS cost function is more accurate and superior to the estimates of both the initial LS cost function and the initial WLS cost function.