/usr/share/octave/packages/signal-1.3.0/levinson.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 | ## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2006 Peter V. Lanspeary, <peter.lanspeary@.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; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{a}, @var{v}, @var{ref}] =} levinson (@var{acf})
## @deftypefnx {Function File} {[@dots{}] =} levinson (@var{acf}, @var{p})
##
## Use the Durbin-Levinson algorithm to solve:
## toeplitz(acf(1:p)) * x = -acf(2:p+1).
## The solution [1, x'] is the denominator of an all pole filter
## approximation to the signal x which generated the autocorrelation
## function acf.
##
## acf is the autocorrelation function for lags 0 to p.
## p defaults to length(acf)-1.
## Returns
## a=[1, x'] the denominator filter coefficients.
## v= variance of the white noise = square of the numerator constant
## ref = reflection coefficients = coefficients of the lattice
## implementation of the filter
## Use freqz(sqrt(v),a) to plot the power spectrum.
##
## REFERENCE
## [1] Steven M. Kay and Stanley Lawrence Marple Jr.:
## "Spectrum analysis -- a modern perspective",
## Proceedings of the IEEE, Vol 69, pp 1380-1419, Nov., 1981
## @end deftypefn
## Based on:
## yulewalker.m
## Copyright (C) 1995 Friedrich Leisch <Friedrich.Leisch@ci.tuwien.ac.at>
## GPL license
## FIXME: Matlab doesn't return reflection coefficients and
## errors in addition to the polynomial a.
## FIXME: What is the difference between aryule, levinson,
## ac2poly, ac2ar, lpc, etc.?
function [a, v, ref] = levinson (acf, p)
if ( nargin<1 )
print_usage;
elseif( ~isvector(acf) || length(acf)<2 )
error( "levinson: arg 1 (acf) must be vector of length >1\n");
elseif ( nargin>1 && ( ~isscalar(p) || fix(p)~=p ) )
error( "levinson: arg 2 (p) must be integer >0\n");
else
if ((nargin == 1)||(p>=length(acf))) p = length(acf) - 1; endif
if( columns(acf)>1 ) acf=acf(:); endif # force a column vector
if nargout < 3 && p < 100
## direct solution [O(p^3), but no loops so slightly faster for small p]
## Kay & Marple Eqn (2.39)
R = toeplitz(acf(1:p), conj(acf(1:p)));
a = R \ -acf(2:p+1);
a = [ 1, a.' ];
v = real( a*conj(acf(1:p+1)) );
else
## durbin-levinson [O(p^2), so significantly faster for large p]
## Kay & Marple Eqns (2.42-2.46)
ref = zeros(p,1);
g = -acf(2)/acf(1);
a = [ g ];
v = real( ( 1 - g*conj(g)) * acf(1) );
ref(1) = g;
for t = 2 : p
g = -(acf(t+1) + a * acf(t:-1:2)) / v;
a = [ a+g*conj(a(t-1:-1:1)), g ];
v = v * ( 1 - real(g*conj(g)) ) ;
ref(t) = g;
endfor
a = [1, a];
endif
endif
endfunction
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