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author | schloegl |
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date | Thu, 02 Apr 2015 10:00:34 +0000 |
parents | 18ff3d258eea |
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function b=ucp(c) % UCP(C) tests if the polynomial C is a Unit-Circle-Polynomial. % It tests if all roots lie inside the unit circle like % B=ucp(C) does the same as % B=all(abs(roots(C))<1) but much faster. % The Algorithm is based on the Jury-Scheme. % C are the elements of the Polynomial % C(1)*X^N + ... + C(N)*X + C(N+1). % % REFERENCES: % O. Foellinger "Lineare Abtastsysteme", Oldenburg Verlag, Muenchen, 1986. % F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993. % $Id$ % Copyright (C) 1996-1999,2008 by Alois Schloegl <alois.schloegl@gmail.com> % % 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/>. [lr,lc] = size(c); % JURY-Scheme b=ones(lr,1); lambda=zeros(lr,1); while (lc > 1), lambda = c(:,lc)./c(:,1); % disp([lc,size(lambda), sum(b),toc]); % ratio must be less then 1 b = b & (abs(lambda) < 1); % and reduced polynomial must be a UCP, too. c(:,1:lc-1) = c(:,1:lc-1) - lambda(:,ones(1,lc-1)).*c(:,lc:-1:2); lc = lc-1; end;