function [h,g,a,info] = wfiltdt_qshift(N)
%WFILTDT_QSHIFT Improved Orthogonality and Symmetry properties
%
% Usage: [h,g,a] = wfiltdt_qshift(N);
%
% [h,g,a]=WFILTDT_QSHIFT(N) with N in {1,2,3,4,5,6,7} returns
% Kingsbury's Q-shift filters suitable for dual-tree complex wavelet
% transform.
% Filters in both trees are orthogonal and based on a single prototype
% low-pass filter with a quarter sample delay. Other filters are
% derived by modulation and time reversal such that they fulfil the
% half-sample delay difference between the trees.
%
% Examples:
% ---------
% :
% wfiltdtinfo('qshift3');
%
% References:
% N. G. Kingsbury. A dual-tree complex wavelet transform with improved
% orthogonality and symmetry properties. In ICIP, pages 375--378, 2000.
%
% N. Kingsbury. Design of q-shift complex wavelets for image processing
% using frequency domain energy minimization. In Image Processing, 2003.
% ICIP 2003. Proceedings. 2003 International Conference on, volume 1,
% pages I--1013--16 vol.1, Sept 2003.
%
%
%
% Url: http://ltfat.github.io/doc/wavelets/wfiltdt_qshift.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR: Zdenek Prusa
[h(:,1),g(:,1),a,info] = wfilt_qshifta(N);
[h(:,2),g(:,2)] = wfilt_qshiftb(N);
% Default first and leaf filters
% They are chosen to be orthonormal near-symmetric here in order not to
% break the orthonormality of the overal representation.
[info.defaultfirst, info.defaultfirstinfo] = fwtinit('symorth1');
[info.defaultleaf, info.defaultleafinfo] = ...
deal(info.defaultfirst,info.defaultfirstinfo);