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