Kingsbury Q

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This example shows that small signal shifts do not significantly change the distribution of energy among the DTCWT coefficients at different scales.

Load an ECG signal. The signal has 2048 samples.

load wecglen = numel(wecg);plot(wecg)axis tight

Create two 1-by-3000 zero vectors. Insert the ECG signal into different segments of each zero vector.

shift1 = 328;shift2 = 368;vec1 = zeros(1,3000);vec2 = zeros(1,3000);vec1(shift1+[1:len]) = wecg;vec2(shift2+[1:len]) = wecg;

Obtain the dual-tree transform of both vectors. Use default settings.

[a1,d1] = dualtree(vec1);[a2,d2] = dualtree(vec2);

Compute the energy at each scale for both decompositions. Note that the energy distribution of the shifted signals across all scales remains approximately the same.

energy1 = cell2mat(cellfun(@(x)(sum(abs(x).^2)),d1,'uni',0));energy2 = cell2mat(cellfun(@(x)(sum(abs(x).^2)),d2,'uni',0));levels =cell(numel(energy1),1);for k=1:numel(energy1)    levels{k} = sprintf('Level %d',k);endenergies = table(levels,energy1,energy2)

energies=11×3 table       levels       energy1    energy2    ____________    _______    _______    {'Level 1' }    16.014     16.014     {'Level 2' }    19.095     19.095     {'Level 3' }     35.99      35.99     {'Level 4' }    25.141     25.065     {'Level 5' }     16.81     17.452     {'Level 6' }    9.7078      9.161     {'Level 7' }    2.3201     2.0513     {'Level 8' }    8.3808     8.4197     {'Level 9' }    23.006      22.56     {'Level 10'}    70.764     73.964     {'Level 11'}    64.097     59.022