makecdjvfilter.sci

小波分解源代码

function [a,b,c] = MakeCDJVFilter(request,digree)
// MakeCDJVFilter --  Set up filters for CDJV Wavelet Transform
//  Usage
//    [a,b,c] = MakeCDJVFilter(request,digree)
//  Inputs
//    request  string: 'HighPass', 'LowPass', 'Precondition', 'Postcondition'
//    digree   integer: 2 or 3 (number of vanishing moments)
//  Outputs
//    a,b,c    filter, left edge filter, right edge filter
//             ('HighPass', 'LowPass')
//    a        conditioning matrix ('Precondition', 'Postcondition')
//
//  Description
//    CDJV have developed an algorithm for wavelets on the interval which
//    preserves the orthogonality, vanishing moments, smoothness, and compact
//    support of Daubechies wavelets on the line.
//
//    The algorithm for wavelets on the interval of CDJV involves four objects
//    not present in the usual periodized algorithm: right edge filters, left
//    edge filters, and pre- and post- conditioning operators.
//
//    These objects are supplied by appropriate requests to MakeCDJVFilter.
//
//  See Also
//    IWT_CDJV, FWT_CDJV, CDJVDyadDown
//
//  References
//    Cohen, Daubechies, Jawerth and Vial, 1992.
//
//  Copyright Aldo I Maalouf

F2 = [  0.482962913145 0.836516303738 0.224143868042 -0.129409522551];
F3 = [  .332670552950, .806891509311, .459877502118, -.135011020010,  ...
-.085441273882, .035226291882 ];
if (request=='HighPass'),
    if digree==2,
         LEHI2 = [ -.7965435153E+00,  .5463927105,  -.2587922607, 0, 0; ...
             .01003722199, .1223510414, .2274281035,  -.8366029193, .4830129294 ];
         REHI2 = [ -.2575129317, .8014229647, -.5398224908, 0, 0 ; ...
              .3717189691, -.3639069552,  -.7175800176, .4010694996, .2315575756 ];
        a = reverse(MirrorFilt(F2)); b = LEHI2; c = REHI2;
     end
     if digree==3,
       LEHI3 = [ .5837810161, .7936188102, .1609551602, -.05884169984, 0, 0, 0, 0 ; ...
                -.3493401755, .2989205708, -.3283012959, -.3322637280, ...
                 .6982497314, -.2878790040, 0, 0; ...
                 .001015059936, -.00003930151414, -.03451437279, -.08486981368, ... 
                 .1337306925,    .4604064313, -.8068932340, .3326712638 ];
        REHI3 = zeros(3,8);
        REHI3(1,1:4) = [   0.07221947896,  -0.42656220040000,   ...
                           0.80423313630,  -0.40747772770000 ];
        REHI3(2,1:6) = [  -0.1535052177,   0.5223942253,  -0.09819804815, ...  
                          -0.7678795675,   0.2985152672,   0.1230738394];
        REHI3(3,:)   = [ 0.2294775468,   -0.4451794532,  -0.2558698634,  ... 
                         0.001694456403,  0.7598761492,   0.1391503023,  ...              
                        -0.2725472621,   -0.1123675794];
        a = reverse(MirrorFilt(F3)); b = LEHI3; c = REHI3;
     end
end
if (request=='LowPass'),
    if digree==2,
         LELO2 = [.6033325147, .6908955290,  -.3983129985, 0, 0 ;   ...
          .3751745208e-01, .4573276687, .8500881006, .2238203490, -.1292227411  ] ;
         RELO2 =  [ .8705087515, .4348970037, .2303890399, 0, 0;
               -.1942333944, .1901514021, .3749553135, .7675566880, .4431490452 ]; 
        a = F2; b = LELO2; c = RELO2;
     end
     if digree==3,
       LELO3 = zeros(3,8);
       LELO3(1,1:4) = [.3888996730 -.08820780195 -.8478413443 .3494874575];
       LELO3(2,1:6) = [ -.6211483347,  .5225274354, -.2000079353, ...
                         .3378673010, -.3997707643,  .1648201271];
       LELO3(3,:) = [  -.009587872354, .0003712272422, .3260097151,  ...
       .8016481698, .4720552497, -.1400420768, -.08542510419, .03521962531 ];
       RELO3 = zeros(3,8);
       RELO3(1,1:4) = [ 0.9096849932 0.3823606566 0.1509872202 0.0589610111];
       RELO3(2,1:6) = [ -0.2904078626, 0.4189992458,  0.4969643833, ...  
                         0.4907578162,  0.4643627531,   0.1914505327 ];
       RELO3(3,:)   = [ 0.08183542639,  -0.1587582353,  -0.09124735588,  ... 
          0.00060427071940, 0.0770293676,   0.520060179,   0.7642591949,  ...  
          0.3150938119 ];
        a = F3; b = LELO3; c = RELO3;
     end
end
if (request=='PreCondition'),
    if digree==2,
      LPREMAT2 = [     .03715799299,     .3248940464   ; ... 
                      1.001445417,       .0000000000  ];
      RPREMAT2 =  [    -.8008131776,      1.089843048 ; ...
                       2.096292891,      .00000000 ];
       a = LPREMAT2; b = flipud(RPREMAT2)'; c = [];
     end
     if digree==3,
       LPREMAT3 = [    -.01509646707, -.5929309617,  .1007941548 ; ...
                        .03068539981,  .2137256750,  .0000000000 ; ...
                       1.000189315,    .0000000000,  .0000000000 ];
     RPREMAT3 = [2.417783369,        -.4658799095,           1.055782523  ;... 
                -6.66336795000000,   1.73763183100000,                  0 ;...
                 5.64221225900000,                  0,                  0 ];
        a = fliplr(LPREMAT3); b = flipud(RPREMAT3)'; c = [];
     end
end
if (request=='PostCondition'),
    if digree==2,
        RPOSTMAT2 = [ .0000000000,    .4770325771 ;
                      .9175633147,    .3505220082 ];
        LPOSTMAT2 = [ 0.000000000,         .9985566693; ...
                      3.077926515,        -.1142044987 ];
        a = LPOSTMAT2; b = flipud(RPOSTMAT2'); c = [];
     end
     if digree==3,
       LPOSTMAT3 = [  .0000000000,  .000000000,  .9998107210 ;...
                      .0000000000, 4.678895037, -.1435465894 ;...
                     9.921210229, 27.52403389,  -.6946792478 ];
       RPOSTMAT3 = [ 0,                0,   0.1772354449 ;...
                     0,     0.5754959032,   0.6796520196 ;...
               0.9471647601,   0.2539462185,  -0.1059694467 ];
        a = flipud(LPOSTMAT3); b = flipud(RPOSTMAT3'); c = [];
     end
end
endfunction