Estimating Parameters of a Sine Wave by Separable Nonlinear Least Squares Fitting

The four-parameter sine wave (FPSW) is commonly used to characterize noise, signal to noise, and the effective number of bits in analog-to-digital converters. An algorithm based on separable nonlinear least squares fitting is presented. In this algorithm, the frequency is the sole iterative variable. Numerical tests show that if the cycle in the record (CiR) is greater than 1, then the convergence is faster and is less dependent on the CiR and SNR. When the CiR is less than one, the convergence is significantly more sensitive to the CiR, the SNR, and the initial phase. Additionally, the lower the frequency, the more difficult the convergence.