The relationship between maximum entropy spectra and maximum likelihood spectra

TLDR: In this article, it was shown that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag.

Abstract: In a long needed paper, R. T. Lacoss (1971) has presented many examples of spectra obtained by the maximum likelihood method and by the maximum entropy method and has shown that these newer techniques are in general superior to the more conventional spectral analysis methods. This short note shows that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag. The data are of this form in almost all practical cases of time series analysis as well as in the special case of wavenumber spectral analysis of wave propagation as seen by a linear array of equally spaced sensors. The wavenumber case will be explicitly considered in this note since it requires the complex variable form of the theory.