Relation between wavelet detail coefficient and magnitude of discontinuity

I am getting a linear correlation between wavelet detail coefficient (at all scales) and magnitude of discontinuity in the signal. Following is an example.

Y=ones(1,1000);
z=zeros(1,50);
for i=1:50
  Y(round(numel(Y)/2))=i;
  [c,l] = wavedec(Y,4,'db7');
  [cd1 cd2 cd3 cd4] = detcoef(c,l,[1 2 3 4]);
  z(i)=min(cd4);
end
plot(z,'*')

I wonder what could be the possible explanation.