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## 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/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{psd},@var{f_out}] =} pburg(@var{x}, @var{poles}, @var{freq}, @var{Fs}, @var{range}, @var{method}, @var{plot_type}, @var{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.
##
## @table @asis
## @item x
## [vector] sampled data
## @item poles
## [integer scalar] required number of poles of the AR model
## @item 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]
## @item Fs
## [real scalar] sampling frequency (Hertz) [default=1]
## @end table
##
## CONTROL-STRING ARGUMENTS -- each of these arguments is a character string.
##
## Control-string arguments can be in any order after the other arguments.
##
##
## @table @asis
## @item 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'.
##
## @item 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.
##
## @item 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.
##
## @item 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
## @end table
##
## RETURNED VALUES:
##
## If return values are not required by the caller, the spectrum
## is plotted and nothing is returned.
##
## @table @asis
## @item psd
## [real vector] power-spectral density estimate
## @item f_out
## [real vector] frequency values
## @end table
##
## HINTS
##
## This function is a wrapper for arburg and ar_psd.
##
## See "help arburg", "help ar_psd".
## @end deftypefn
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;
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