Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / tsa-4.2.4 / lpc.m

diff --git a/octave_packages/tsa-4.2.4/lpc.m b/octave_packages/tsa-4.2.4/lpc.m
new file mode 100644 (file)
index 0000000..ffd60c2
--- /dev/null
+++ b/octave_packages/tsa-4.2.4/lpc.m
@@ -0,0 +1,71 @@
+function [A] = lpc(Y,P,mode);
+% LPC Linear prediction coefficients 
+% The Burg-method is used to estimate the prediction coefficients
+%
+% A = lpc(Y [,P]) finds the coefficients  A=[ 1 A(2) ... A(N+1) ],
+%      of an Pth order forward linear predictor
+%     
+%       Xp(n) = -A(2)*X(n-1) - A(3)*X(n-2) - ... - A(N+1)*X(n-P)
+%          
+%      such that the sum of the squares of the errors
+%              
+%       err(n) = X(n) - Xp(n)
+%             
+%      is minimized.  X can be a vector or a matrix.  If X is a matrix
+%       containing a separate signal in each column, LPC returns a model
+%      estimate for each column in the rows of A. N specifies the order
+%      of the polynomial A(z).
+%                                     
+%      If you do not specify a value for P, LPC uses a default P = length(X)-1.
+%
+%
+% see also ACOVF ACORF AR2POLY RC2AR DURLEV SUMSKIPNAN LATTICE 
+% 
+
+% REFERENCE(S):
+%  J.P. Burg, "Maximum Entropy Spectral Analysis" Proc. 37th Meeting of the Society of Exp. Geophysiscists, Oklahoma City, OK 1967
+%  J.P. Burg, "Maximum Entropy Spectral Analysis" PhD-thesis, Dept. of Geophysics, Stanford University, Stanford, CA. 1975.
+%  P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+%  S.   Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+%  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
+%  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+%      $Id: lpc.m 5090 2008-06-05 08:12:04Z schloegl $
+%      Copyright (C) 1996-2002,2008 by Alois Schloegl <a.schloegl@ieee.org>
+%       This is part of the TSA-toolbox. See also 
+%       http://hci.tugraz.at/schloegl/matlab/tsa/
+%
+%    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/>.
+
+
+[yr,yc] = size(Y);
+if yr < yc,
+       fprintf(2,'Warning LCP: data vector Y must be a column not a row vector\n');
+end;
+
+if nargin < 2,
+        P = yr-1;
+end;
+
+% you can use any of the following routines. 
+% the lattice methods are preferable for stochastic time series. 
+% but can fail for deterministic signals see: 
+% http://sourceforge.net/mailarchive/message.php?msg_name=20080516115110.GB20642%40localhost
+
+% [AR,RC,PE] = lattice(Y.',P);         % Burg method
+% [AR,RC,PE] = lattice(Y.',P,'GEOL');  % geometric lattice
+[AR,RC,PE] = durlev(acovf(Y.',P));     % Yule-Walker
+
+A = ar2poly(AR);
+