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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...

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Published in:	IEEE transactions on instrumentation and measurement 2010-12, Vol.59 (12), p.3214-3217
Main Author:	Chen, Kui Fu
Format:	Article
Language:	English
Subjects:	Algorithms Analog-digital conversion Convergence Convergence of numerical methods Fittings four-parameter sine wave (FPSW) Frequency Instrumentation Iterative algorithms Least squares approximation least squares error Least squares method Least squares methods Noise Nonlinear equations Nonlinearity Parameter estimation separable nonlinear least squares (NLS) fitting Sine waves Sole Testing
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description	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.
doi_str_mv	10.1109/TIM.2010.2047298
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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. 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source	IEEE Electronic Library (IEL) Journals
subjects	Algorithms Analog-digital conversion Convergence Convergence of numerical methods Fittings four-parameter sine wave (FPSW) Frequency Instrumentation Iterative algorithms Least squares approximation least squares error Least squares method Least squares methods Noise Nonlinear equations Nonlinearity Parameter estimation separable nonlinear least squares (NLS) fitting Sine waves Sole Testing
title	Estimating Parameters of a Sine Wave by Separable Nonlinear Least Squares Fitting
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