TABLE OF CONTENTS One of the most popular approaches in linear prediction spectrum estimation is the Burg method, and it has also been called the maximum entropy method (MEM). If there are n points of data from x(0) to x( N - 1) and p + 1 lags of autocorrelations from R(0) to R( p), Burg suggested that the unknown autocorrelation lags from R( p + 1), R( p + 2), can be extrapolated from the input data points. There are an infinite number of ways to extrapolate the autocorrelations. Burg further suggested that the extrapolation of the autocorrelations should not add any new information arbitrarily to the sequence. The information is measured in terms of entropy from Shannon's theorem. Maximizing the entropy implies that the time series is in the most random state and no new information is arbitrarily added to the series. Thus, the name MEM is used.
Later investigators showed that in order to use the MEM, the autocorrelation of the time series must be known. However, the data obtained from most experiments are, in general, a series of real or complex values as a function of time. In other words, the only known data are the time series but not the autocorrelations of the input signal. The autocorrelations calculated using the time series are not the true values, but only estimations. Thus, the promise of the MEM is...
