durbinlevinson.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 1995  Friedrich Leisch
##
## This file is part of Octave.
##
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## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
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## 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 Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} durbinlevinson (@var{c}, @var{oldphi}, @var{oldv})
## Perform one step of the Durbin-Levinson algorithm.
##
## The vector @var{c} specifies the autocovariances @code{[gamma_0, ...,
## gamma_t]} from lag 0 to @var{t}, @var{oldphi} specifies the
## coefficients based on @var{c}(@var{t}-1) and @var{oldv} specifies the
## corresponding error.
##
## If @var{oldphi} and @var{oldv} are omitted, all steps from 1 to
## @var{t} of the algorithm are performed.
## @end deftypefn

## Author: FL <[e-mail]>
## Description: Perform one step of the Durbin-Levinson algorithm

function [newphi, newv] = durbinlevinson (c, oldphi, oldv)

  if (! ((nargin == 1) || (nargin == 3)))
    print_usage ();
  endif

  if (columns (c) > 1)
    c=c';
  endif

  newphi = 0;
  newv = 0;

  if (nargin == 3)

    t = length (oldphi) + 1;

    if (length (c) < t+1)
      error ("durbilevinson: c too small");
    endif

    if (oldv == 0)
      error ("durbinlevinson: oldv = 0");
    endif

    if (rows (oldphi) > 1)
      oldphi = oldphi';
    endif

    newphi = zeros (1, t);
    newphi(1) = (c(t+1) - oldphi * c(2:t)) / oldv;
    for i = 2 : t
      newphi(i) = oldphi(i-1) - newphi(1) * oldphi(t-i+1);
    endfor
    newv = (1 - newphi(1)^2) * oldv;

  elseif(nargin == 1)

    tt = length (c)-1;
    oldphi = c(2) / c(1);
    oldv = (1 - oldphi^2) * c(1);

    for t = 2 : tt

      newphi = zeros (1, t);
      newphi(1) = (c(t+1) - oldphi * c(2:t)) / oldv;
      for i = 2 : t
        newphi(i) = oldphi(i-1) - newphi(1) * oldphi(t-i+1);
      endfor
      newv = (1 - newphi(1)^2) * oldv;

      oldv = newv;
      oldphi = newphi;

    endfor

  endif

endfunction

/*
@GROUP
signal
@SYNTAX
durbinlevinson()
@DOC
.
@EXAMPLES
.
@NOTES
.
@SEE
bartlett, hamming, hanning
*/