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function LS = symlift(wname)
%SYMLIFT Symlets lifting schemes.
% LS = SYMLIFT(WNAME) returns the lifting scheme specified
% by WNAME. The valid values for WNAME are:
% 'sym2', 'sym3', 'sym4', 'sym5', 'sym6', 'sym7', 'sym8'
%
% A lifting scheme LS is a N x 3 cell array such that:
% for k = 1:N-1
% | LS{k,1} is the lifting "type" 'p' (primal) or 'd' (dual).
% | LS{k,2} is the corresponding lifting filter.
% | LS{k,3} is the higher degree of the Laurent polynomial
% | corresponding to the previous filter LS{k,2}.
% LS{N,1} is the primal normalization.
% LS{N,2} is the dual normalization.
% LS{N,3} is not used.
%
% For more information about lifting schemes type: lsinfo.
% M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 12-Jun-2003.
% Last Revision: 20-Dec-2010.
% Copyright 1995-2010 The MathWorks, Inc.
Num = wstr2num(wname(4:end));
switch Num
%== sym2 ============================================================%
case 2
LS = {...
'd',-sqrt(3),0; ...
'p',[sqrt(3)-2 sqrt(3)]/4,1; ...
'd',1,-1 ...
};
LS(end+1,:) = {(sqrt(3)+1)/sqrt(2),(sqrt(3)-1)/sqrt(2),[]};
% %-------------------- Num LS = 1 ----------------------%
% LS = {...
% 'd' [ -1.7320508075722079] 0
% 'p' [ -0.0669872981075236 0.4330127018915160] 1
% 'd' [ 0.9999999999994959] -1
% [ 1.9318516525804916] [ 0.5176380902044105] []
% };
case 2.1
%-------------------- Num LS = 2 ----------------------%
LS = {...
'd' -0.5773502691885155 1
'p' [0.2009618943233436 0.4330127018926641] 0
'd' -0.3333333333327671 0
1.1153550716496254 0.8965754721686846 []
};
case 2.2
%-------------------- Num LS = 3 ----------------------%
LS = {...
'd' 0.5773502691900463 0
'p' [ -0.4330127018915159 2.7990381056783082] 0
'd' -0.3333333333332407 1
0.2988584907223872 3.3460652149545598 []
};
case 2.3
%-------------------- Num LS = 4 ----------------------%
LS = {...
'd' 1.7320508075676158 1
'p' [ -0.4330127018926641 -0.9330127018941287] -1
'd' 0.9999999999980750 2
-0.5176380902041495 -1.9318516525814655 []
};
%== sym3 ============================================================%
case 3
%-------------------- Num LS = 4 ----------------------%
LS = {...
'd' 0.4122865950085308 0
'p' [ -0.3523876576801823 1.5651362801993258] 0
'd' [ -0.4921518447467098 -0.0284590895616518] 1
'p' 0.3896203901445617 0
0.5213212719156450 1.9182029467652528 []
};
case 3.1
%-------------------- Num LS = 2 ----------------------%
LS = {...
'd' -0.4122865950517414 1
'p' [ 0.4667569466389586 0.3523876576432496] 0
'd' [ -0.4921518449249469 0.0954294390155849] 0
'p' -0.1161930919191620 1
0.9546323126334674 1.0475237290484967 []
};
case 3.2
%-------------------- Num LS = 5 ----------------------%
LS = {...
'd' -0.4122865950517414 1
'p' [ -1.5651362796324981 0.3523876576432496] 0
'd' [ -2.5381416988469603 0.4921518449249469] 1
'p' 0.3896203899372190 -1
4.9232611941772104 0.2031173973021602 []
};
case 3.3
%-------------------- Num LS = 6 ----------------------%
LS = {...
'd' 2.4254972441665452 1
'p' [ -0.3523876576432495 -0.2660422349436360] -1
'd' [ 2.8953474539232271 0.1674258735039567] 2
'p' -0.0662277660392190 -1
-1.2644633083567955 -0.7908493614571760 []
};
%== sym4 ============================================================%
case 4
%-------------------- Num LS = 16 ----------------------%
LS = {...
'd' 0.3911469419700402 0
'p' [ -0.1243902829333865 -0.3392439918649451] 1
'd' [ -1.4195148522334731 0.1620314520393038] 0
'p' [ 0.4312834159749964 0.1459830772565225] 0
'd' -1.0492551980492930 1
1.5707000714496564 0.6366587855802818 []
};
case 4.1
%-------------------- Num LS = 19 ----------------------%
LS = {...
'd' -0.3911469419692201 1
'p' [ 0.3392439918656564 0.1243902829339031] -1
'd' [ -0.1620314520386309 -0.8991460629746448] 2
'p' [ 0.4312834159764773 -0.2304688357916146] -1
'd' 0.6646169843776997 2
1.2500817546829417 0.7999476804248136 []
};
%== sym5 ============================================================%
case 5
%-------------------- Num LS = 29 ----------------------%
LS = {...
'd' -0.9259329171294208 0
'p' [ 0.4985231842281166 0.1319230270282341] 0
'd' [ -0.4293261204657586 -1.4521189244206130] 1
'p' [ -0.0948300395515551 0.2804023843755281] 1
'd' [ 1.9589167118877153 0.7680659387165244] 0
'p' -0.1726400850543451 0
2.0348614718930915 0.4914339446751972 []
};
case 5.1
%-------------------- Num LS = 23 ----------------------%
LS = {...
'd' 1.0799918455239754 0
'p' [ 0.1131044403334987 -0.4985231842281165] 1
'd' [ 2.4659476305614541 -0.5007584249312305] 0
'p' [ -0.0558424247659369 -0.2404034797205558] 1
'd' [ 3.3265774193213002 1.3043080355478955] 0
'p' -0.1016623108755641 0
-2.6517078902691829 -0.3771154446044534 []
};
case 5.2
%-------------------- Num LS = 24 ----------------------%
LS = {...
'd' 1.0799918455239754 0
'p' [ 0.1131044403334987 -0.4985231842281165] 1
'd' [ -1.6937259364035369 -0.5007584249312305] 0
'p' [ 0.2404034797205558 -0.0813027019760201] 0
'd' [ 0.8958585825127051 -4.4713044896913088] 1
'p' 0.1480132819787044 0
3.0742840094152357 0.3252789907950670 []
};
case 6
%-------------------- Num LS = 1 ----------------------%
% Pow MAX = 0 - diff POW = 0
%---+----+----+----+----+---%
LS = {...
'd' 0.2266091476053614 0
'p' [ 1.2670686037583443 -0.2155407618197651] 1
'd' [ -0.5047757263881194 4.2551584226048398] -1
'p' [ -0.0447459687134724 -0.2331599353469357] 3
'd' [ 18.3890008539693710 -6.6244572505007815] -3
'p' [ -0.1443950619899142 0.0567684937266291] 5
'd' 5.5119344180654508 -5
-1.6707087396895259 -0.5985483742581210 []
};
case 7
%-------------------- Num LS = 1 ----------------------%
% Pow MAX = 0 - diff POW = 0
%---+----+----+----+----+---%
LS = {...
'p' 0.3905508237124110 0
'd' [ -0.3388639272262041 7.1808202373094066] 0
'p' [ -0.0139114610261505 -0.1372559452118446] 2
'd' [ 29.6887047769035310 0.1338899561610895] -2
'p' [ 0.1284625939282921 -0.0001068796412094] 4
'd' [ -7.4252008608107740 -2.3108058612546007] -4
'p' [ 0.0532700919298021 0.2886088139333021] 6
'd' -1.1987518309831993 -6
2.1423821239872392 0.4667701381576485 []
};
case 8
%-------------------- Num LS = 1 ----------------------%
% Pow MAX = 0 - diff POW = 0
%---+----+----+----+----+---%
LS = {...
'd' 0.1602796165947262 0
'p' [ 0.7102593464144563 -0.1562652322408773] 1
'd' [ -0.4881496179387070 1.8078532235524318] -1
'p' [ 1.7399180943774144 -0.4863315213006700] 3
'd' [ -0.5686365236759819 -0.2565755576271975] -3
'p' [ -0.8355308510520870 3.7023086183759020] 5
'd' [ 0.5881022226370752 -0.3717452749902822] -5
'p' [ -2.1580699620177337 0.7491890598341392] 7
'd' 0.3531271830147090 -7
0.4441986800900797 2.2512448704197152 []
};
otherwise
error(message('Wavelet:FunctionArgVal:Invalid_WavNum'))
end