## Copyright (C) 2006 Peter V. Lanspeary <pvl@mecheng.adelaide.edu.au>
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.

## usage:
##    [psd,f_out] = pburg(x,poles,freq,Fs,range,method,plot_type,criterion)
##
## Calculate Burg maximum-entropy power spectral density.
## The functions "arburg" and "ar_psd" do all the work.
## See "help arburg" and "help ar_psd" for further details.
##
## ARGUMENTS:
##     All but the first two arguments are optional and may be empty.
##   x       %% [vector] sampled data
##
##   poles   %% [integer scalar] required number of poles of the AR model
##
##   freq    %% [real vector] frequencies at which power spectral density
##           %%               is calculated
##           %% [integer scalar] number of uniformly distributed frequency
##           %%          values at which spectral density is calculated.
##           %%          [default=256]
##
##   Fs      %% [real scalar] sampling frequency (Hertz) [default=1]
##
##
## CONTROL-STRING ARGUMENTS -- each of these arguments is a character string.
##   Control-string arguments can be in any order after the other arguments.
##
##
##   range   %% 'half',  'onesided' : frequency range of the spectrum is
##           %%       from zero up to but not including sample_f/2.  Power
##           %%       from negative frequencies is added to the positive
##           %%       side of the spectrum.
##           %% 'whole', 'twosided' : frequency range of the spectrum is
##           %%       -sample_f/2 to sample_f/2, with negative frequencies
##           %%       stored in "wrap around" order after the positive
##           %%       frequencies; e.g. frequencies for a 10-point 'twosided'
##           %%       spectrum are 0 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2 -0.1
##           %% 'shift', 'centerdc' : same as 'whole' but with the first half
##           %%       of the spectrum swapped with second half to put the
##           %%       zero-frequency value in the middle. (See "help
##           %%       fftshift". If "freq" is vector, 'shift' is ignored.
##           %% If model coefficients "ar_coeffs" are real, the default
##           %% range is 'half', otherwise default range is 'whole'.
##
##   method  %% 'fft':  use FFT to calculate power spectral density.
##           %% 'poly': calculate spectral density as a polynomial of 1/z
##           %% N.B. this argument is ignored if the "freq" argument is a
##           %%      vector.  The default is 'poly' unless the "freq"
##           %%      argument is an integer power of 2.
##
## plot_type %% 'plot', 'semilogx', 'semilogy', 'loglog', 'squared' or 'db':
##           %% specifies the type of plot.  The default is 'plot', which
##           %% means linear-linear axes. 'squared' is the same as 'plot'.
##           %% 'dB' plots "10*log10(psd)".  This argument is ignored and a
##           %% spectrum is not plotted if the caller requires a returned
##           %% value.
##
## criterion %% [optional string arg]  model-selection criterion.  Limits
##           %%       the number of poles so that spurious poles are not
##           %%       added when the whitened data has no more information
##           %%       in it (see Kay & Marple, 1981). Recognized values are
##           %%  'AKICc' -- approximate corrected Kullback information
##           %%             criterion (recommended),
##           %%   'KIC'  -- Kullback information criterion
##           %%   'AICc' -- corrected Akaike information criterion
##           %%   'AIC'  -- Akaike information criterion
##           %%   'FPE'  -- final prediction error" criterion
##           %% The default is to NOT use a model-selection criterion
##
## RETURNED VALUES:
##     If return values are not required by the caller, the spectrum
##     is plotted and nothing is returned.
##   psd       %% [real vector] power-spectral density estimate
##   f_out     %% [real vector] frequency values
##
## HINTS
##   This function is a wrapper for arburg and ar_psd.
##   See "help arburg", "help ar_psd".

function [psd,f_out]=pburg(x,poles,varargin)

  ##
  if ( nargin<2 )
    error( 'pburg: need at least 2 args. Use "help pburg"' );
  endif
  nvarargin=length(varargin);
  criterion=[];
  ##
  ## Search for a "criterion" arg. If found, remove it
  ## from "varargin" list and feed it to arburg instead.
  for iarg = 1: nvarargin
    arrgh = varargin{iarg};
    if ( ischar(arrgh) && ( strcmp(arrgh,'AKICc') ||...
         strcmp(arrgh,'KIC') || strcmp(arrgh,'AICc') ||...
         strcmp(arrgh,'AIC') || strcmp(arrgh,'FPE') ) )
      criterion=arrgh;
      if ( nvarargin>1 )
        varargin{iarg}= [];
      else
        varargin={};
      endif
    endif
  endfor
  ##
  [ar_coeffs,residual]=arburg(x,poles,criterion);
  if ( nargout==0 )
    ar_psd(ar_coeffs,residual,varargin{:});
  elseif ( nargout==1 )
    psd = ar_psd(ar_coeffs,residual,varargin{:});
  elseif ( nargout>=2 )
    [psd,f_out] = ar_psd(ar_coeffs,residual,varargin{:});
  endif

endfunction

%!demo
%! a = [1.0 -1.6216505 1.1102795 -0.4621741 0.2075552 -0.018756746];
%! Fs = 25;
%! n = 16384;
%! signal = detrend (filter (0.70181, a, rand (1, n)));
%! % frequency shift by modulating with exp(j.omega.t)
%! skewed = signal .* exp (2*pi*i*2/Fs*[1:n]);
%! hold on;
%! pburg (signal, 3, [], Fs);
%! pburg (signal, 4, [], Fs, "whole");
%! pburg (signal, 5, 128, Fs, "shift", "semilogy");
%! pburg (skewed, 7, 128, Fs, "AKICc", "shift", "semilogy");
%! user_freq = [-0.2:0.02:0.2]*Fs;
%! pburg (skewed, 7, user_freq, Fs, "AKICc", "semilogy");
%! hold off;
