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Estimation of Equispaced Sinusoids Using Maximum Likelihood Method

P. Pajunen,J. Joutsensalo,Juha Karhunen,Kari Saarinen-1995-01-01
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TL;DRAbstract

A signal composed of sinusoids equispaced in frequency appears in certain applications. One such applicationis fault detection of rotating machines. We propose maximum likelihood method for estimating the spacing of frequencies, when the number of samples is to be minimised. The application of maximum likelihood method is feasible because the equispaced property of the signal allows easy maximization of the likelihood function in one dimensional parameter space. Using this approach, the number of samples required for reliable estimation of the power spectrum can be reduced dramatically compared to the Fourier-based methods used previously, such as the Welch method.

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A signal composed of sinusoids equispaced in frequency appears in certain applications. One such applicationis fault detection of rotating machines. We propose maximum likelihood method for estimating the spacing of frequencies, when the number of samples is to be minimised. The application of maximum likelihood method is feasible because the equispaced property of the signal allows easy maximization of the likelihood function in one dimensional parameter space. Using this approach, the number of samples required for reliable estimation of the power spectrum can be reduced dramatically compared to the Fourier-based methods used previously, such as the Welch method.

Keywords

Maximum likelihoodMaximizationMathematicsMaximum likelihood sequence estimationLikelihood functionAlgorithmSIGNAL (programming language)Expectation–maximization algorithm

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