symlift.m
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上传日期：2013-01-09
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文件大小：12k
- 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: 30-Jun-2003.
- % Copyright 1995-2004 The MathWorks, Inc.
- % $Revision: 1.1.6.2 $ $Date: 2004/03/15 22:41:50 $
- 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('Invalid wavelet number.')
-
- end
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