trigpol

  TRIGPOL generate trigonometric polynomial.

          TRIGPOL(N) generates the following polynomial in e^jw:
          
          P(e^jw)=sum(k=0,...,N-1){ (N-1+k) ( e^(-jw) - 2 + e^jw )
                                       k 
          
          The output of the function is a vector of size 2*N-1 holding
          the coefficients corresponding to the different powers of e^jw. 

          See also: NUMCOMB, DAUB, SPLINE

0001 function polinomio=trigpol(N)
0002 
0003 %  TRIGPOL generate trigonometric polynomial.
0004 %
0005 %          TRIGPOL(N) generates the following polynomial in e^jw:
0006 %
0007 %          P(e^jw)=sum(k=0,...,N-1){ (N-1+k) ( e^(-jw) - 2 + e^jw )
0008 %                                       k
0009 %
0010 %          The output of the function is a vector of size 2*N-1 holding
0011 %          the coefficients corresponding to the different powers of e^jw.
0012 %
0013 %          See also: NUMCOMB, DAUB, SPLINE
0014 
0015 
0016 %--------------------------------------------------------
0017 % Copyright (C) 1994, 1995, 1996, by Universidad de Vigo
0018 %
0019 %
0020 % Uvi_Wave is free software; you can redistribute it and/or modify it
0021 % under the terms of the GNU General Public License as published by the
0022 % Free Software Foundation; either version 2, or (at your option) any
0023 % later version.
0024 %
0025 % Uvi_Wave is distributed in the hope that it will be useful, but WITHOUT
0026 % ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
0027 % FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
0028 % for more details.
0029 %
0030 % You should have received a copy of the GNU General Public License
0031 % along with Uvi_Wave; see the file COPYING.  If not, write to the Free
0032 % Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
0033 %
0034 %       Author: Nuria Gonzalez Prelcic
0035 %       e-mail: Uvi_Wave@tsc.uvigo.es
0036 %--------------------------------------------------------
0037 
0038 
0039 %The polynomial is constructed from a sum.
0040 %coefs holds the coefficients of each term in the sum.
0041 
0042 coefs=zeros(N,2*N-1);
0043 coefs(1,N)=1;
0044 
0045  
0046 for i=1:N-1
0047     fila=[1 -2 1];
0048     for j=2:i
0049         fila=conv(fila,[1 -2 1]);
0050     end;
0051     fila=numcomb(N-1+i,i)*(-0.25)^i*fila;
0052     fila=[ zeros(1,(N-i-1))  fila zeros(1,(N-i-1))];
0053     coefs(i+1,:)=fila;
0054 end
0055 
0056 for i=0:(2*(N-1))
0057     polinomio(i+1)=0;
0058     for j=1:N
0059         polinomio(i+1)=polinomio(i+1)+coefs(j,i+1);
0060     end
0061 end;