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C
C
C
      SUBROUTINE BURG(LX,X,F,B,LA,A,M,S,Y,TABLE)
C
C
C***BEGIN PROLOGUE  BURG
C***DATE WRITTEN  1979 ?
C***REVISION DATE  11 OCTOBER 1983
C***CATEGORY NO.  L10F
C***KEYWORDS  SPECTRAL ANALYSIS, MAXIMUM ENTROPY METHOD
C***AUTHOR   MANUAL T. SILVIA
C            U.S. NAVAL UNDERWATER SYSTEMS CENTER
C            NEWPORT, RHODE ISLAND
C***PURPOSE  BURG CALCULATES THE MAXIMUM ENTROPY SPECTRUM
C            OF A REAL, UNIVARIATE TIME SERIES (OF EQUALLY
C            SPACED SAMPLE POINTS).
C***DESCRIPTION
C
C   BURG computes the coefficients of a finite length causal
C   forward or backward prediction filter, and uses both the
C   forward and backward predictions in a symmetric manner to
C   generate the Maximum Entropy Spectrum by means of a Toeplitz
C   recursion.
C
C   This program was copied from the book "Deconvolution of
C   Geophysical Time Series in the Exploration for Oil and
C   Natural Gas", by Manuel T. Silvia and Enders A. Robinson,
C   Elsevier Scientific Publishing Company, New York, 1979.
C   A more complete description of the algorithm and program
C   can be found in that work.  A few very minor modifications
C   were made in October, 1983 by Bert W. Rust of the Scientific
C   Computing Division, National Bureau of Standards.
C
C
C   I N P U T
C   ---------
C
C   LX      Length of the input time series.
C
C   X       Vector (of length LX) containing the input time series.
C
C   LA      Length of prediction filter to use in calculating
C           the spectrum.  LA should be less than LX.
C
C   M       A small integer which determines the number of frequency
C           points at which the spectrum is estimated.  The spectrum
C           will be estimated at  1 + 2**(M-1)  equally spaced
C           frequencies, with the first frequency being 0.0 and the
C           final frequency being the Nyquist frequency (reciprocal of
C           twice the sample interval).  Thus if the sample interval
C           is 1 time unit and M = 9, then the spectral estimate
C           will be calculated at 257 equally spaced frequencies
C           between  0.0  and  0.5.
C
C
C   O U T P U T
C   -----------
C
C   S       Vector of length  (2**(M-1) + 1)  containing the
C           Maximum Entropy spectral estimates.
C
C
C   M I S C E L L A N E O U S
C   -------------------------
C
C   F , B   Working vectors of length LX.
C
C   A , Y   Working vectors of length  2**M.
C
C   TABLE   Working vector of length  2**(M-2) + 1.
C
C
C***REFERENCE  M.T. Silvia and E.A. Robinson, "Deconvolution of
C                Geophysical Time Series in the Exploration for
C                Oil and Natural Gas," Elsevier, New York, 1979.
C
C***ROUTINES CALLED  COSQTB, FFTBRG
C***END PROLOGUE  BURG
C
C
