Sinusoidal Parameter Estimation Using Roots of an Algebraic Equation

Takahiro MURAKAMI  Yoshihisa ISHIDA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.7   pp.1487-1496
Publication Date: 2011/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1487
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
sinusoidal parameter,  frequency estimation,  minimization problem,  local minima,  

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Summary: 
An algorithm for estimating sinusoidal parameters is presented. In this paper, it is assumed that an observed signal is a single sinusoidal signal contaminated by white Gaussian noise. Based on this assumption, the sinusoidal parameters can be found by minimizing a cost function using the mean squared error (MSE) between the observed signal and a sinusoidal signal with arbitrary sinusoidal parameters. Because the cost function is nonlinear and not convex, it has undesirable local minima. To solve the minimization problem, we propose to use the roots of an algebraic equation. The algebraic equation is derived straightforwardly from the cost function. We show that the global solution is formulated by using the roots of the algebraic equation.