LH-ESTIMATE OF COMPLEX HARMONIC FREQUENCY
DOI:
https://doi.org/10.18372/2310-5461.26.8715Keywords:
maximum likelihood, complex harmonic signal, frequency estimation, linear regressionAbstract
The problem of estimation the frequency of a harmonic single-tone signal is relevant in many technical applications: radio monitoring, radar and acoustics, measurement of mechanical vibrations, geophysical signals. Modern radio devices operate with quadrature process that mathematically leads to complex signals processing. The analytical synthesis of the frequency estimate in the article is based on the classical maximum likelihood (ML) method. With the asymptotic assumption of a large ratio of signal to white Gaussian noise power the problem is reduced to a system of two linear equations. It contains the unknown frequency and phase, and the input data consists of full phases of input counts. The calculation algorithm is obtained in explicit analytic form suitable for practical implementation. It is shown that the same system of equations is obtained by the least squares method when frequency is considered as a slope coefficient of a linear regression model of the full phase of the signal. Therefore, the heuristically proposed Tretter’s frequency estimate is a special case of the synthesized ML-estimate of the frequency of the complex harmonic.
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