INTRODUCTION

In the first “published” reference on maximum entropy spectra, an enormously influential and seminal symposium reprint, Burg (1967) announced his new method based upon exactly known, error free autocorrelation samples. Burg showed that if the first n samples were indeed the beginning of a legitimate autocorrelation function (ACF) that the next sample (n+1) was restricted to lie in a very small range. If that (n+1) sample were chosen to be in the center of the allowed range, then the sample number (n+2) would have the greatest freedom to be chosen, again in a small range. In the same paper, Burg also showed that the extrapolation to the center point of the permissable range corresponds to a maximum entropy situation in which the available data were fully utilized, while no unwarranted assumptions were made about unavailable data. In fact unmeasured data were to be as random as possible subject to the constraint that the power spectral density produce ACF values in agreement with the known, exact ACF.

Some time later it was recognized that the realization of exactly known ACF values rarely if ever occurs in practice and that the ACF is usually estimated from a few samples of the time series or from some other experimental arrangement and is therefore subject to measurement error. Thus the concept of exact matching of given ACF values was weakened to approximate matching: up to the error variance.