ivan@78: function [h_0,h_1] = daubcqf(N,TYPE)
ivan@78: %    [h_0,h_1] = daubcqf(N,TYPE); 
ivan@78: %
ivan@78: %    Function computes the Daubechies' scaling and wavelet filters
ivan@78: %    (normalized to sqrt(2)).
ivan@78: %
ivan@78: %    Input: 
ivan@78: %       N    : Length of filter (must be even)
ivan@78: %       TYPE : Optional parameter that distinguishes the minimum phase,
ivan@78: %              maximum phase and mid-phase solutions ('min', 'max', or
ivan@78: %              'mid'). If no argument is specified, the minimum phase
ivan@78: %              solution is used.
ivan@78: %
ivan@78: %    Output: 
ivan@78: %       h_0 : Minimal phase Daubechies' scaling filter 
ivan@78: %       h_1 : Minimal phase Daubechies' wavelet filter 
ivan@78: %
ivan@78: %    Example:
ivan@78: %       N = 4;
ivan@78: %       TYPE = 'min';
ivan@78: %       [h_0,h_1] = daubcqf(N,TYPE)
ivan@78: %       h_0 = 0.4830 0.8365 0.2241 -0.1294
ivan@78: %       h_1 = 0.1294 0.2241 -0.8365 0.4830
ivan@78: %
ivan@78: %    Reference: "Orthonormal Bases of Compactly Supported Wavelets",
ivan@78: %                CPAM, Oct.89 
ivan@78: %
ivan@78: 
ivan@78: %File Name: daubcqf.m
ivan@78: %Last Modification Date: 01/02/96	15:12:57
ivan@78: %Current Version: daubcqf.m	2.4
ivan@78: %File Creation Date: 10/10/88
ivan@78: %Author: Ramesh Gopinath  <ramesh@dsp.rice.edu>
ivan@78: %
ivan@78: %Copyright (c) 2000 RICE UNIVERSITY. All rights reserved.
ivan@78: %Created by Ramesh Gopinath, Department of ECE, Rice University. 
ivan@78: %
ivan@78: %This software is distributed and licensed to you on a non-exclusive 
ivan@78: %basis, free-of-charge. Redistribution and use in source and binary forms, 
ivan@78: %with or without modification, are permitted provided that the following 
ivan@78: %conditions are met:
ivan@78: %
ivan@78: %1. Redistribution of source code must retain the above copyright notice, 
ivan@78: %   this list of conditions and the following disclaimer.
ivan@78: %2. Redistribution in binary form must reproduce the above copyright notice, 
ivan@78: %   this list of conditions and the following disclaimer in the 
ivan@78: %   documentation and/or other materials provided with the distribution.
ivan@78: %3. All advertising materials mentioning features or use of this software 
ivan@78: %   must display the following acknowledgment: This product includes 
ivan@78: %   software developed by Rice University, Houston, Texas and its contributors.
ivan@78: %4. Neither the name of the University nor the names of its contributors 
ivan@78: %   may be used to endorse or promote products derived from this software 
ivan@78: %   without specific prior written permission.
ivan@78: %
ivan@78: %THIS SOFTWARE IS PROVIDED BY WILLIAM MARSH RICE UNIVERSITY, HOUSTON, TEXAS, 
ivan@78: %AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, 
ivan@78: %BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 
ivan@78: %FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL RICE UNIVERSITY 
ivan@78: %OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 
ivan@78: %EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
ivan@78: %PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; 
ivan@78: %OR BUSINESS INTERRUPTIONS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, 
ivan@78: %WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR 
ivan@78: %OTHERWISE), PRODUCT LIABILITY, OR OTHERWISE ARISING IN ANY WAY OUT OF THE 
ivan@78: %USE OF THIS SOFTWARE,  EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
ivan@78: %
ivan@78: %For information on commercial licenses, contact Rice University's Office of 
ivan@78: %Technology Transfer at techtran@rice.edu or (713) 348-6173
ivan@78: 
ivan@78: if(nargin < 2),
ivan@78:   TYPE = 'min';
ivan@78: end;
ivan@78: if(rem(N,2) ~= 0),
ivan@78:   error('No Daubechies filter exists for ODD length');
ivan@78: end;
ivan@78: K = N/2;
ivan@78: a = 1;
ivan@78: p = 1;
ivan@78: q = 1;
ivan@78: h_0 = [1 1];
ivan@78: for j  = 1:K-1,
ivan@78:   a = -a * 0.25 * (j + K - 1)/j;
ivan@78:   h_0 = [0 h_0] + [h_0 0];
ivan@78:   p = [0 -p] + [p 0];
ivan@78:   p = [0 -p] + [p 0];
ivan@78:   q = [0 q 0] + a*p;
ivan@78: end;
ivan@78: q = sort(roots(q));
ivan@78: qt = q(1:K-1);
ivan@78: if TYPE=='mid',
ivan@78:   if rem(K,2)==1,  
ivan@78:     qt = q([1:4:N-2 2:4:N-2]);
ivan@78:   else
ivan@78:     qt = q([1 4:4:K-1 5:4:K-1 N-3:-4:K N-4:-4:K]);
ivan@78:   end;
ivan@78: end;
ivan@78: h_0 = conv(h_0,real(poly(qt)));
ivan@78: h_0 = sqrt(2)*h_0/sum(h_0); 	%Normalize to sqrt(2);
ivan@78: if(TYPE=='max'),
ivan@78:   h_0 = fliplr(h_0);
ivan@78: end;
ivan@78: if(abs(sum(h_0 .^ 2))-1 > 1e-4) 
ivan@78:   error('Numerically unstable for this value of "N".');
ivan@78: end;
ivan@78: h_1 = rot90(h_0,2);
ivan@78: h_1(1:2:N)=-h_1(1:2:N);