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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Bibliographic Details
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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Summary: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.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2010.2047298