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function varargout = dtfilters(name,type)
%DTFILTERS Dual-Tree filters
% [DF,RF] = DTFILTERS(NAME) returns the decomposition filters
% and the associated reconstruction filters which name
% is given by the string NAME.
%
% The valid values for NAME are:
% - 'dtfP':
% returns the filters for the first step and the
% following steps, for dual-tree ('FSfarras' for the first
% step and 'qshiftN' with P = 1, 2, 3 or 4 corresponding
% to N = 6, 10, 14 or 18 for the following steps) .
%
% - 'dddtf1':
% returns the filters for the first step and the
% following steps, for double density dual-tree
% ('FSdoubledualfilt' and 'doubledualfilt').
%
% - 'self1','self2':
% I W. Selesnick - 3-channel perfect reconstruction
% filter bank
%
% - 'filters1','filters2': NOT DOCUMENTED []
% 3-channel perfect reconstruction filter bank
%
% - 'farras','FSfarras' (first step filter):
% nearly symmetric filters for orthogonal
% 2-channel perfect reconstruction filter bank
%
% - 'qshiftN' with N = 6, 10, 14 or 18
% Kingsbury Q-filters for the dual-tree complex DWT
%
% - 'doubledualfilt','FSdoubledualfilt' (first step filter):
% DF and RF are cell arrays of 3-channel filter bank
%
% - 'AntonB': NOT DOCUMENTED []
%
% - Orthogonal or biorthogonal wavelet names (see WFILTERS)
%
% F = DTFILTERS(NAME,TYPE) returns the following filters:
% Decomposition filters if type = 'd'
% Reconstruction filters if type = 'r'
%
% See also WFILTERS
%
%----------------------------------------------------------
%REFERENCES
%----------------------------------------------------------
% farras nearly symmetric filters for orthogonal
% 2-channel perfect reconstruction filter bank
% REF 1:
% A. F. Abdelnour and I. W. Selesnick.
% "Nearly symmetric orthogonal wavelet bases",
% Proc. IEEE Int. Conf. Acoust., Speech,
% Signal Processing (ICASSP), May 2001.
%----------------------------------------------------------
% REF 2:
% N. G. Kingsbury, "A dual-tree complex wavelet
% transform with improved orthogonality and symmetry
% properties", Proceedings of the IEEE Int. Conf. on
% Image Proc. (ICIP), 2000
%----------------------------------------------------------
% 3-channel perfect reconstruction filter bank
% Symmetric Filters for the Double-Density Wavelet Transform
% REF 3:
% I. W. Selesnick and A. Farras Abdelnour.
% Symmetric wavelet tight frames with two generators.
% Applied and Computational Harmonic Analalysis, 17(2), 2004.
%----------------------------------------------------------
% REF 4:
% The Double-Density Dual-Tree Discrete Wavelet Transform
% Ivan W. Selesnick
% July 27, 2001
% Electrical Engineering, Polytechnic University
% Multirate Processing and Wavelets
%----------------------------------------------------------
% M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 09-Nov-2012.
% Last Revision: 11-Apr-2013.
% Copyright 1995-2013 The MathWorks, Inc.
name = lower(name);
ok = true;
if isequal(name(1),'q')
try
ok = isequal(name(1:6),'qshift');
numFilt = str2double(name(7:end));
if ~ismember(numFilt,[6 10 14 18]) ,
ok = false;
else
name = 'qshift';
end
catch
ok = false;
end
if ~ok
msg = getWavMSG('Wavelet:moreMSGRF:Invalid_Wavelet',name);
error(msg);
end
elseif isequal(name(1:2),'dt')
try
ok = isequal(name(1:3),'dtf');
numFilt = str2double(name(4:end));
if ~ismember(numFilt,1:4) ,
ok = false;
else
name = 'dtf';
end
catch
ok = false;
end
end
if ~ok
msg = getWavMSG('Wavelet:moreMSGRF:Invalid_Wavelet',name);
error(msg);
end
switch name
case 'dtf'
[Df_FS,Rf_FS] = dtfilters('Fsfarras');
switch numFilt
case 1 , [Df_next,Rf_next] = dtfilters('qshift6');
case 2 , [Df_next,Rf_next] = dtfilters('qshift10');
case 3 , [Df_next,Rf_next] = dtfilters('qshift14');
case 4 , [Df_next,Rf_next] = dtfilters('qshift18');
end
Df = {Df_FS,Df_next};
Rf = {Rf_FS,Rf_next};
case 'dddtf1'
[Df_FS,Rf_FS] = dtfilters('FSdoubledualfilt');
[Df_next,Rf_next] = dtfilters('doubledualfilt');
Df = {Df_FS,Df_next};
Rf = {Rf_FS,Rf_next};
case 'self1'
H = [...
0.06911582051268 0.00007342378571 0.00016216892384
0.35966127039020 0.00038207883303 0.00084388611367
0.66578510237730 -0.00598664482533 -0.01366169688553
0.46591894334945 -0.03433855126018 -0.07812787935415
-0.01910143987094 -0.05544284199193 -0.08404354646603
-0.13775229565904 0.00187143276342 0.22307058313047
-0.00879228135716 0.13862717458070 0.39450869604392
0.01947949838578 0.33211688782429 -0.65664993171756
0.00009957952467 -0.56616644388191 0.21389772021137
-0.00020063527985 0.18886348417221 0
];
G = [...
0.01382316410254 0.00036711892855 0.00081084461919
0.18251756689833 0.00484734559355 0.01070618752183
0.55379561515138 0.01295727262146 0.02642247548195
0.64032052013227 -0.00610823096768 -0.04248472459154
0.20240253780720 -0.06568401496723 -0.20956025899924
-0.13270357516508 -0.09685196235772 -0.00551846607616
-0.07143784469173 -0.02112084546363 0.65041073668340
0.01797544572026 0.54923548323017 -0.47356633868171
0.00852330881716 -0.41541486345192 0.04277954404227
-0.00100317639923 0.03777269683444 0
];
Df_FS{1} = H;
Df_FS{2} = G;
Rf_FS{1} = Df_FS{1}(end:-1:1,:);
Rf_FS{2} = Df_FS{2}(end:-1:1,:);
Df = {Df_FS,Df_FS};
Rf = {Rf_FS,Rf_FS};
case 'self2'
H = [...
0.01167515006693 0.00000028033779 0.00000096316386
0.11210453438921 0.00000269179728 0.00000924827821
0.39020359888747 -0.00009458242812 -0.00032856572032
0.63766002212216 -0.00098283172247 -0.00341136920868
0.45159271169876 -0.00322600807907 -0.00984858347245
-0.01779052717512 -0.00339847237922 0.00114352817725
-0.18995098895800 0.00534784540227 0.05358462859672
-0.03633171373566 0.02694106074718 0.07100034042574
0.05116380416058 0.04999293344040 -0.07326560617712
0.01309797742830 -0.00764246645306 -0.23356729557382
-0.00814108745277 -0.21155330115108 -0.04788025853496
-0.00163786108717 -0.13672353553244 0.58084573581233
0.00056506737003 0.61809721274879 -0.40145448519473
0.00000434924483 -0.39817251892698 0.06317171942796
-0.00000147458644 0.06141169219871 0
0 0 0
];
G = [...
0.00166787858099 0.00000196236451 0.00000674214701
0.04270099078000 0.00005024041316 0.00017261229964
0.23192413512891 0.00023596311036 0.00078545980855
0.54594099119669 -0.00030264225957 -0.00168611304984
0.60903833681124 -0.00443438247636 -0.01814247165657
0.21459366376196 -0.01230171877677 -0.03508479826925
-0.16295875588933 -0.01563309030618 0.01806298323729
-0.12839582439678 0.00449550768918 0.13569634310037
0.03096765367958 0.07816842450995 0.09808771813111
0.03738202154037 0.13192700814758 -0.19634137757248
-0.00385258125359 -0.12443537362415 -0.37624919671465
-0.00531066009030 -0.44659309709664 0.56741070948369
0.00033043623380 0.57729947000603 -0.20174314229173
0.00019559839462 -0.19725137058663 0.00902453134685
-0.00001032210505 0.00877309888553 0
0 0 0
];
Df_FS{1} = H;
Df_FS{2} = G;
Rf_FS{1} = Df_FS{1}(end:-1:1,:);
Rf_FS{2} = Df_FS{2}(end:-1:1,:);
Df = {Df_FS,Df_FS};
Rf = {Rf_FS,Rf_FS};
case 'filters1'
Df = [
0.14301535070442 -0.01850334430500 -0.04603639605741
0.51743439976158 -0.06694572860103 -0.16656124565526
0.63958409200212 -0.07389654873135 0.00312998080994
0.24429938448107 0.00042268944277 0.67756935957555
-0.07549266151999 0.58114390323763 -0.46810169867282
-0.05462700305610 -0.42222097104302 0
];
Rf = Df(end:-1:1, :);
case 'filters2' %% NOMME filter1 dans l'article!? %%
% 3-channel perfect reconstruction filter bank
% Symmetric Filters for the Double-Density Wavelet Transform Reference:
% I. W. Selesnick and A. Farras Abdelnour.
% Symmetric wavelet tight frames with two generators.
% Applied and Computational Harmonic Analalysis, 17(2), 2004.
Df = [
0.00069616789827 -0.00014203017443 0.00014203017443
-0.02692519074183 0.00549320005590 -0.00549320005590
-0.04145457368920 0.01098019299363 -0.00927404236573
0.19056483888763 -0.13644909765612 0.07046152309968
0.58422553883167 -0.21696226276259 0.13542356651691
0.58422553883167 0.33707999754362 -0.64578354990472
0.19056483888763 0.33707999754362 0.64578354990472
-0.04145457368920 -0.21696226276259 -0.13542356651691
-0.02692519074183 -0.13644909765612 -0.07046152309968
0.00069616789827 0.01098019299363 0.00927404236573
0 0.00549320005590 0.00549320005590
0 -0.00014203017443 -0.00014203017443
];
Rf = Df(end:-1:1, :);
case 'farras'
% farras nearly symmetric filters for orthogonal
% 2-channel perfect reconstruction filter bank
% REFERENCE:
% A. F. Abdelnour and I. W. Selesnick.
% "Nearly symmetric orthogonal wavelet bases",
% Proc. IEEE Int. Conf. Acoust., Speech,
% Signal Processing (ICASSP), May 2001.
Df = [
0 -0.01122679215254
0 0.01122679215254
-0.08838834764832 0.08838834764832
0.08838834764832 0.08838834764832
0.69587998903400 -0.69587998903400
0.69587998903400 0.69587998903400
0.08838834764832 -0.08838834764832
-0.08838834764832 -0.08838834764832
0.01122679215254 0
0.01122679215254 0
];
Rf = Df(end:-1:1, :);
case 'fsfarras'
% Farras filters organized for the dual-tree complex DWT.
% Df{i}, i = 1,2 - Decomposition filters for tree i
% Rf{i}, i = 1,2 - Reconstruction filters for tree i
Df{1} = [
0 0
-0.08838834764832 -0.01122679215254
0.08838834764832 0.01122679215254
0.69587998903400 0.08838834764832
0.69587998903400 0.08838834764832
0.08838834764832 -0.69587998903400
-0.08838834764832 0.69587998903400
0.01122679215254 -0.08838834764832
0.01122679215254 -0.08838834764832
0 0
];
Rf{1} = Df{1}(end:-1:1, :);
Df{2} = [
0.01122679215254 0
0.01122679215254 0
-0.08838834764832 -0.08838834764832
0.08838834764832 -0.08838834764832
0.69587998903400 0.69587998903400
0.69587998903400 -0.69587998903400
0.08838834764832 0.08838834764832
-0.08838834764832 0.08838834764832
0 0.01122679215254
0 -0.01122679215254
];
Rf{2} = Df{2}(end:-1:1, :);
case {'qshift'}
% Kingsbury Q-filters for the dual-tree complex DWT
%
% OUTPUT:
% Df{i}, i = 1,2 - analysis filters for tree i
% Rf{i}, i = 1,2 - synthesis filters for tree i
% note: Df{2} is the reverse of Df{1}
% REFERENCE:
% N. G. Kingsbury, "A dual-tree complex wavelet
% transform with improved orthogonality and symmetry
% properties", Proceedings of the IEEE Int. Conf. on
% Image Proc. (ICIP), 2000
% These cofficients are rounded to 8 decimal places.
switch numFilt
case 6
Df{1} = [
0.03516384000000 0
0 0
-0.08832942000000 -0.11430184000000
0.23389032000000 0
0.76027237000000 0.58751830000000
0.58751830000000 -0.76027237000000
0 0.23389032000000
-0.11430184000000 0.08832942000000
0 0
0 -0.03516384000000
];
Df{2} = [
0 -0.03516384000000
0 0
-0.11430184000000 0.08832942000000
0 0.23389032000000
0.58751830000000 -0.76027237000000
0.76027237000000 0.58751830000000
0.23389032000000 0
-0.08832942000000 -0.11430184000000
0 0
0.03516384000000 0
];
case 10
Df{1} = [
0.051130405283832 -0.006181881892116
-0.013975370246889 0.001689681272528
-0.109836051665971 -0.100231219507476
0.263839561058938 -0.000873622695217
0.766628467793037 0.563655710127052
0.563655710127052 -0.766628467793037
0.000873622695217 0.263839561058938
-0.100231219507476 0.109836051665971
-0.001689681272528 -0.013975370246889
-0.006181881892116 -0.051130405283832
];
Df{2} = [
-0.006181881892116 -0.051130405283832
-0.001689681272528 -0.013975370246889
-0.100231219507476 0.109836051665971
0.000873622695217 0.263839561058938
0.563655710127052 -0.766628467793037
0.766628467793037 0.563655710127052
0.263839561058938 -0.000873622695217
-0.109836051665971 -0.100231219507476
-0.013975370246889 0.001689681272528
0.051130405283832 -0.006181881892116
];
case 14
Df{1} = [
0.003253142763653 -0.004556895628475
-0.003883211999158 0.005439475937274
0.034660346844853 0.017025223881554
-0.038872801268828 -0.023825384794920
-0.117203887699115 -0.106711804686665
0.275295384668882 -0.011866092033797
0.756145643892522 0.568810420712123
0.568810420712123 -0.756145643892522
0.011866092033797 0.275295384668882
-0.106711804686665 0.117203887699115
0.023825384794920 -0.038872801268828
0.017025223881554 -0.034660346844853
-0.005439475937274 -0.003883211999158
-0.004556895628475 -0.003253142763653
];
Df{2} = [
-0.004556895628475 -0.003253142763653
-0.005439475937274 -0.003883211999158
0.017025223881554 -0.034660346844853
0.023825384794920 -0.038872801268828
-0.106711804686665 0.117203887699115
0.011866092033797 0.275295384668882
0.568810420712123 -0.756145643892522
0.756145643892522 0.568810420712123
0.275295384668882 -0.011866092033797
-0.117203887699115 -0.106711804686665
-0.038872801268828 -0.023825384794920
0.034660346844853 0.017025223881554
-0.003883211999158 0.005439475937274
0.003253142763653 -0.004556895628475
];
case 18
Df{1} = [
-0.002284127440271 0.002411869456666
0.001209894163073 -0.001277558653807
-0.011834794515431 -0.002576174306601
0.001283456999344 0.006628794612430
0.044365221606617 0.031526377122085
-0.053276108803047 -0.018156493945546
-0.113305886362143 -0.120188544710795
0.280902863222186 -0.024550152433667
0.752816038087856 0.565808067396459
0.565808067396459 -0.752816038087856
0.024550152433667 0.280902863222186
-0.120188544710795 0.113305886362143
0.018156493945546 -0.053276108803047
0.031526377122085 -0.044365221606617
-0.006628794612430 0.001283456999344
-0.002576174306601 0.011834794515431
0.001277558653807 0.001209894163073
0.002411869456666 0.002284127440271
];
Df{2} = [
0.002411869456666 0.002284127440271
0.001277558653807 0.001209894163073
-0.002576174306601 0.011834794515431
-0.006628794612430 0.001283456999344
0.031526377122085 -0.044365221606617
0.018156493945546 -0.053276108803047
-0.120188544710795 0.113305886362143
0.024550152433667 0.280902863222186
0.565808067396459 -0.752816038087856
0.752816038087856 0.565808067396459
0.280902863222186 -0.024550152433667
-0.113305886362143 -0.120188544710795
-0.053276108803047 -0.018156493945546
0.044365221606617 0.031526377122085
0.001283456999344 0.006628794612430
-0.011834794515431 -0.002576174306601
0.001209894163073 -0.001277558653807
-0.002284127440271 0.002411869456666
];
end
Rf{1} = Df{1}(end:-1:1, :);
Rf{2} = Df{2}(end:-1:1, :);
case 'doubledualfilt'
% Df - cell array containing analysis filters
% Df{1} - analysis filters for tree 1
% Df{2} - analysis filters for tree 2
% Rf - cell array containing synthesis filters
% Rf{1} - synthesis filters for tree 1
% Rf{2} - synthesis filters for tree 2
Df{1} = [
0.00017870679071 -0.00012344587034 0.00001437252392
-0.02488304194507 0.01718853971559 -0.00200122286479
0.00737700819766 -0.00675291099550 0.00027261232228
0.29533805776119 0.02671809818132 0.06840460220387
0.59529279993637 -0.64763513288874 0.01936710587994
0.45630440337458 0.47089724990858 -0.68031992557818
0.11239376309619 0.16040017815754 0.42976785708978
-0.01971220693439 -0.01484700537727 0.11428688385011
-0.00813549683439 -0.00588868840296 0.05057805218407
0.00005956893024 0.00004311757177 -0.00037033761102
];
Df{2} = [
0.00005956893024 0.00004311757177 -0.00037033761102
-0.00813549683439 -0.00588868840296 0.05057805218407
-0.01971220693439 -0.01484700537727 0.11428688385011
0.11239376309619 0.16040017815754 0.42976785708978
0.45630440337458 0.47089724990858 -0.68031992557818
0.59529279993637 -0.64763513288874 0.01936710587994
0.29533805776119 0.02671809818132 0.06840460220387
0.00737700819766 -0.00675291099550 0.00027261232228
-0.02488304194507 0.01718853971559 -0.00200122286479
0.00017870679071 -0.00012344587034 0.00001437252392
];
% Swap the two highpass filters for Df{2}
tmp = Df{2}(:,2);
Df{2}(:,2) = Df{2}(:,3);
Df{2}(:,3) = tmp;
Rf{1} = Df{1}(end:-1:1,:);
Rf{2} = Df{2}(end:-1:1,:);
case 'fsdoubledualfilt'
% OUTPUT:
% Df - cell array containing analysis filters
% Df{1} - analysis filters for tree 1
% Df{2} - analysis fitlers for tree 2
% Rf - cell array containing synthesis filters
% Rf{1} - synthesis filters for tree 1
% Rf{2} - synthesis filters for tree 2
Df{1} = [
0 0 0
0.00069616789827 -0.00014203017443 0.00014203017443
-0.02692519074183 0.00549320005590 -0.00549320005590
-0.04145457368920 0.01098019299363 -0.00927404236573
0.19056483888763 -0.13644909765612 0.07046152309968
0.58422553883167 -0.21696226276259 0.13542356651691
0.58422553883167 0.33707999754362 -0.64578354990472
0.19056483888763 0.33707999754362 0.64578354990472
-0.04145457368920 -0.21696226276259 -0.13542356651691
-0.02692519074183 -0.13644909765612 -0.07046152309968
0.00069616789827 0.01098019299363 0.00927404236573
0 0.00549320005590 0.00549320005590
0 -0.00014203017443 -0.00014203017443
0 0 0
];
Df{2} = [
0 0 0
0 0 0
0.00069616789827 -0.00014203017443 0.00014203017443
-0.02692519074183 0.00549320005590 -0.00549320005590
-0.04145457368920 0.01098019299363 -0.00927404236573
0.19056483888763 -0.13644909765612 0.07046152309968
0.58422553883167 -0.21696226276259 0.13542356651691
0.58422553883167 0.33707999754362 -0.64578354990472
0.19056483888763 0.33707999754362 0.64578354990472
-0.04145457368920 -0.21696226276259 -0.13542356651691
-0.02692519074183 -0.13644909765612 -0.07046152309968
0.00069616789827 0.01098019299363 0.00927404236573
0 0.00549320005590 0.00549320005590
0 -0.00014203017443 -0.00014203017443
];
Rf{1} = Df{1}(end:-1:1, :);
Rf{2} = Df{2}(end:-1:1, :);
case 'antonb'
D = [ ...
0 0
0.02674875741081 0
-0.01686411844287 0
-0.07822326652899 0.04563588155712
0.26686411844288 -0.02877176311425
0.60294901823636 -0.29563588155712
0.26686411844287 0.55754352622850
-0.07822326652899 -0.29563588155713
-0.01686411844287 -0.02877176311425
0.02674875741081 0.04563588155712
0 0
0 0
];
R = 2*[ ...
0 0
0 0.02674875741081
0 0.01686411844287
-0.04563588155712 -0.07822326652899
-0.02877176311425 -0.26686411844288
0.29563588155712 0.60294901823636
0.55754352622850 -0.26686411844287
0.29563588155713 -0.07822326652899
-0.02877176311425 0.01686411844287
-0.04563588155712 0.02674875741081
0 0
0 0
];
DD = [
0 0
0 0
0.02674875741081 0
-0.01686411844287 0
-0.07822326652899 0.04563588155712
0.26686411844288 -0.02877176311425
0.60294901823636 -0.29563588155712
0.26686411844287 0.55754352622850
-0.07822326652899 -0.29563588155713
-0.01686411844287 -0.02877176311425
0.02674875741081 0.04563588155712
0 0
];
RR = 2*[ ...
0 0.02674875741081
0 0.01686411844287
-0.04563588155712 -0.07822326652899
-0.02877176311425 -0.26686411844288
0.29563588155712 0.60294901823636
0.55754352622850 -0.26686411844287
0.29563588155713 -0.07822326652899
-0.02877176311425 0.01686411844287
-0.04563588155712 0.02674875741081
0 0
0 0
0 0
];
Df{1} = [D(:,1) D(:,2)]; Df{2} = [DD(:,1) DD(:,2)];
Rf{1} = [R(:,1) R(:,2)]; Rf{2} = [RR(:,1) RR(:,2)];
otherwise
try
[LO_D,HI_D,LO_R,HI_R] = wfilters(name);
Df = [LO_D' HI_D'];
Rf = [LO_R' HI_R'];
catch %#ok<CTCH>
msg = getWavMSG('Wavelet:moreMSGRF:Invalid_Wavelet',name);
error(msg);
end
end
if nargin <2
varargout = {Df,Rf};
else
if isequal(lower(type),'d') , varargout = {Df};
elseif isequal(lower(type),'r') , varargout = {Rf};
else varargout = {Df,Rf};
end
end