%% definition of wavelet functions
D2 = [1,    1];
D4 = [0.6830127,    1.1830127,  0.3169873,  -0.1830127];
D6 = [0.47046721,   1.14111692, 0.650365,   -0.19093442,    -0.12083221,    0.0498175];
D8 = [0.32580343,   1.01094572, 0.8922014,  -0.03957503,    -0.26450717,    0.0436163,  0.0465036,  -0.01498699];
D10 = [0.22641898,  0.85394354, 1.02432694, 0.19576696, -0.34265671,    -0.04560113,    0.10970265, -0.0088268, -0.01779187,    0.004717428];
D12 = [0.15774243,  0.69950381, 1.06226376, 0.44583132, -0.3199866, -0.18351806,    0.13788809, 0.03892321, -0.04466375,    0.000783251,    0.006756062,    -0.001523534];
D14 = [0.11009943,  0.56079128, 1.03114849, 0.66437248, -0.20351382,    -0.31683501,    0.1008467,  0.11400345, -0.05378245,    -0.02343994,    0.01774979, 0.000607515,    -0.002547905,   0.000500227];
D16 = [0.07695562,  0.44246725, 0.95548615, 0.82781653, -0.02238574,    -0.40165863,    0.000668194,    0.18207636, -0.0245639, -0.06235021,    0.01977216, 0.01236884, -0.006887719,   -0.000554005,   0.00095523, -0.000166137];
D18 = [0.05385035,  0.3448343,  0.85534906, 0.92954571, 0.18836955, -0.41475176,    -0.13695355,    0.21006834, 0.043452675,    -0.09564726,    0.000354893,    0.03162417, -0.00667962,    -0.006054961,   0.002612967,    0.000325815,    -0.00035633,    5.56455E-05];
D20 = [0.03771716,  0.26612218, 0.74557507, 0.97362811, 0.39763774, -0.3533362, -0.27710988,    0.18012745, 0.13160299, -0.10096657,    -0.04165925,    0.04696981, 0.005100437,    -0.015179,  0.001973325,    0.002817687,    -0.000969948,   -0.000164709,   0.000132354,    -1.87584E-05];


%% setup h0 and h1
name = 'D4';
h0 = D4;
h1 = fliplr(h0);
idx = 2:2:numel(h0);
h1(idx) = -h1(idx);

%% iterate
scale = [1];
figure;
for i = 0:100
    h0scaled = zeros(1, numel(h0)*(2^i));
    h1scaled = zeros(1, numel(h1)*(2^i));
    for j = 1:numel(h0)
       h0scaled(j*(2^i)) = h0(j);
       h1scaled(j*(2^i)) = h1(j);
    end
    wavelet = conv(scale,h1scaled);
    scale   = conv(scale,h0scaled);
    stairs(scale);
    hold all;
    title(['Scale function ' name ' iteration ' int2str(i)]);
    stairs(wavelet);
    hold off;
    title(['Wavelet function ' name ' iteration ' int2str(i)]);
    pause;
end