lemarie

LEMARIE    Generates the quadrature filters given by Battle and Lemarie.

        [H,G,RH,RG] = LEMARIE (NUM_COEFS) returns the coeficients of
        orthonormal  Battle-Lemarie wavelets. NUM_COEFS specifies the
           number of coefficients. 

        H is the analysis lowpass filter, RH the synthesis lowpass 
        filter, G the analysis higthpass filter and RG the synthesis
        highpass filter.

        References: S. Mallat, "A Theory for Multiresolution Signal
                Decomposition: The Wavelet Representation", IEEE Trans.
            on Patt. An. and Mach. Intell., July 1989

 $Id: lemarie.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $

0001 function  [h,g,rh,rg]=lemarie(num_coefs)
0002 
0003 %LEMARIE    Generates the quadrature filters given by Battle and Lemarie.
0004 %
0005 %        [H,G,RH,RG] = LEMARIE (NUM_COEFS) returns the coeficients of
0006 %        orthonormal  Battle-Lemarie wavelets. NUM_COEFS specifies the
0007 %           number of coefficients.
0008 %
0009 %        H is the analysis lowpass filter, RH the synthesis lowpass
0010 %        filter, G the analysis higthpass filter and RG the synthesis
0011 %        highpass filter.
0012 %
0013 %        References: S. Mallat, "A Theory for Multiresolution Signal
0014 %                Decomposition: The Wavelet Representation", IEEE Trans.
0015 %            on Patt. An. and Mach. Intell., July 1989
0016 %
0017 % $Id: lemarie.m,v 1.1 2004/09/26 04:00:24 matthewbrett Exp $
0018 
0019 %--------------------------------------------------------
0020 % Copyright (C) 1994, 1995, 1996, by Universidad de Vigo
0021 %
0022 %
0023 % Uvi_Wave is free software; you can redistribute it and/or modify it
0024 % under the terms of the GNU General Public License as published by the
0025 % Free Software Foundation; either version 2, or (at your option) any
0026 % later version.
0027 %
0028 % Uvi_Wave is distributed in the hope that it will be useful, but WITHOUT
0029 % ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
0030 % FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
0031 % for more details.
0032 %
0033 % You should have received a copy of the GNU General Public License
0034 % along with Uvi_Wave; see the file COPYING.  If not, write to the Free
0035 % Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
0036 %
0037 %       Author: Jose Martin Garcia
0038 %       e-mail: Uvi_Wave@tsc.uvigo.es
0039 %--------------------------------------------------------
0040 
0041 
0042 % frequency axis
0043 L=128;
0044 w=[0:2*pi/L:2*pi*(1-1/L)];
0045 w(1)=eps;
0046 w(65)=w(65)+1e-15;
0047 
0048 % calculation of frequency response of analysis lowpass filter
0049 num=0;den=0;
0050 K=36;
0051 for k=-K:K,
0052     num=1./((w+2*pi*k).^8)+num;
0053     den=1./((2*w+2*pi*k).^8)+den;
0054 end
0055 H=sqrt(num./(2.^8*den));
0056 H(1)=1;
0057 
0058 % obtain the time response of lowpass filter
0059 h=real(ifft(H,L));
0060 h=[ h(128-floor(num_coefs/2)+1:128) h(1:ceil(num_coefs/2))];
0061 h=sqrt(2)/sum(h)*h;
0062 
0063 [rh,rg,h,g]=rh2rg(fliplr(h));