Mercurial > hg > smallbox
view util/Rice Wavelet Toolbox/daubcqf.m @ 190:759313488e7b luisf_dev
Added two config files for the 2 step dic and learn scripts; removed 'extra' folder; created init script (initial version).
author | luisf <luis.figueira@eecs.qmul.ac.uk> |
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date | Tue, 13 Mar 2012 17:33:20 +0000 |
parents | f69ae88b8be5 |
children |
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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) 348-6173 if(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);