% toon0311          
% toon0312          
% toon0333          
% toon0334
% toon0335

infoStr= ...
    ['                                                            '
     ' Some Popular Wavelets: Haar, Daubechies,                   '
     ' Coiflet, and Symmlet.                                      '
     '                                                            '];
infoStr
pause;


%
        wave = MakeWavelet(4,8,'Haar',[],'Mother',1024);
        subplot(221);
        t = (1:1024)./1024;
        plot(t(300:800),wave(300:800)); title(' Haar Wavelet ');
%
        wave = MakeWavelet(4,8,'Daubechies',4,'Mother',1024);
        subplot(222);
        plot(t(300:800),wave(300:800)); title(' D4 Wavelet ');
%
        wave = MakeWavelet(4,8,'Coiflet',3,'Mother',1024);
        subplot(223);
        plot(t(300:800),wave(300:800)); title(' C3 Coiflet ');
%
        wave = MakeWavelet(4,8,'Symmlet',8,'Mother',1024);
        subplot(224);
        plot(t(300:800),wave(300:800)); title(' S8 Symmlet ');

pause
infoStr= ...
    ['                                                            '
     ' Wavelet Transform of Doppler Signal                        '
     ' Coiflet 3,                                                 '
     '                                                            '];

        dop = MakeSignal('Doppler', 256 );
        qmf = MakeONFilter('Coiflet',3);
        wcDopp   = FWT_PO(dop,1,qmf);
%
        t  = (1:256) ./256;
        subplot(211); plot(t, dop);  title('Doppler')
        subplot(212); PlotWaveCoeff(wcDopp,1,1.);   title('WT Dopp')

%--------------------
pause
infoStr= ...
    ['                                                            '
     ' MRA of Doppler                                             '
     ' Haar wavelet                                               '
     '                                                            '];

        dop = MakeSignal('Doppler', 256 );
        qmf = MakeONFilter('Haar');
        wcDopp   = FWT_PO(dop,1,qmf);
%
        t  = (1:256) ./256;
        subplot(121); plot(t, dop);  title('Doppler')
        subplot(122);  PlotMultiRes(wcDopp ,1,0.,qmf);  title('MRA Dopp')
pause
infoStr= ...
    ['                                                            '
     ' MRA of Doppler                                             '
     ' Coiflet 3,                                                 '
     '                                                            '];
        qmf = MakeONFilter('Coiflet', 3);
        wcDopp   = FWT_PO(dop,2,qmf);
%
        t  = (1:256) ./256;
        subplot(121); plot(t, dop);  title('Doppler')
        subplot(122);  PlotMultiRes(wcDopp ,2,0.,qmf);  title('MRA Dopp')
pause


%---------------------------------------------------------
infoStr= ...
    ['                                                            '
     ' Wavelet Transform and Singularities                        '
     '  Here we analyze 4 functions:                              '
     '         Ramp = t - (t >= .37);                             '
     '      Crease = exp(-4*abs(t - .37));                        '
     '        Cusp = sqrt(abs(t - .37));                          '
     '        Sing = 1 ./abs(t - (k+.5)/2048);                    '
     '   These have singularities of degree 0, 1, 1/2, and -1,    '
     '   respectively.                                            '
     '                                                            '];


infoStr
pause
% toon0331 -- Behavior of Wavelet Transform of Singularities
%
%     Here we analyze 4 functions:
%
%             Ramp = t - (t >= .37);
%           Crease = exp(-4*abs(t - .37));
%             Cusp = sqrt(abs(t - .37));
%             Sing = 1 ./abs(t - (k+.5)/2048);
%
%     These have singularities of degree 0, 1, 1/2, and -1,
%        respectively.
%
        clear t;
        n = 4096;
        t  = (1:n) ./n;
        Ramp = t - (t >= .37);
        Crease = exp(-4*abs(t - .37));
        Cusp = sqrt(abs(t - .37));
        k = floor(n * .37);
        Sing = 1 ./abs(t - (k+.5)/n); Sing = Sing ./ norm(Sing) .* 20;
%
        subplot(221); plot(t, Sing);  title(' Sing')
        subplot(222); plot(t, Ramp);   title(' Ramp')
        subplot(223); plot(t, Cusp);  title(' Cusp')
        subplot(224); plot(t, Crease); title(' Crease')

pause
%--------------------
% toon0332 -- Behavior of Wavelet Transform of Singularities
%
%       Show the wavelet transforms of the signals in toon0331.
% 
%             Away from the singularities, 
%               the wavelet coefficients decay rapidly
%
        qmf = MakeONFilter('Coiflet',3);
        wcRamp   = FWT_PO(Ramp,3,qmf);
        wcCrease = FWT_PO(Crease,3,qmf);
        wcCusp   = FWT_PO(Cusp,3,qmf);
        wcSing   = FWT_PO(Sing,3,qmf);
%
        subplot(221); PlotWaveCoeff(wcSing,3,0.);  title('WT Sing')
        subplot(222); PlotWaveCoeff(wcRamp,3,2.);   title('WT Ramp')
        subplot(223); PlotWaveCoeff(wcCusp,3,2.);  title('WT Cusp')
        subplot(224); PlotWaveCoeff(wcCrease,3,2.); title('WT Crease')

% Repeat again!--------------------
pause
        subplot(421); plot(t, Sing);  title(' Sing')
        subplot(422); plot(t, Ramp);   title(' Ramp')
        subplot(425); plot(t, Cusp);  title(' Cusp')
        subplot(426); plot(t, Crease); title(' Crease')
        subplot(423); PlotWaveCoeff(wcSing,3,0.);  title('WT Sing')
        subplot(424); PlotWaveCoeff(wcRamp,3,2.);   title('WT Ramp')
        subplot(427); PlotWaveCoeff(wcCusp,3,2.);  title('WT Cusp')
        subplot(428); PlotWaveCoeff(wcCrease,3,2.); title('WT Crease')
pause

       % toon0333 -- Behavior of Wavelet Transform of Singularities
% 
%       Show the MRA's of the signals in toon0331.
%
        qmf = MakeONFilter('Coiflet',3);
        wcRamp   = FWT_PO(Ramp,3,qmf);
        wcCrease = FWT_PO(Crease,3,qmf);
        wcCusp   = FWT_PO(Cusp,3,qmf);
        wcSing   = FWT_PO(Sing,3,qmf);
%
        subplot(221); PlotMultiRes(wcRamp  ,3,2.,qmf);  title('MR Ramp')
        subplot(222); PlotMultiRes(wcCrease,3,2.,qmf);  title('MR Crease')
        subplot(223); PlotMultiRes(wcCusp  ,3,2.,qmf);  title('MR Cusp')
        subplot(224); PlotMultiRes(wcSing  ,3,0.,qmf);  title('MR Sing')