%% Create folding of two rectangular impulses with spiky function
X=-2.3:0.0005:3.8;
F1=exp(-X);
F1(X<=0) = 0;
F2=zeros(size(X)); F2(abs(X)<=0.5) = 1;
clf

[tmp zero_offset] = min(abs(X));

!rm -f /tmp/conv_box_spike*
integral=nan(size(X));
for offset_i=1:numel(X)
  offset=X(offset_i);
  shift=offset_i-zero_offset;
  F2_shifted = circshift(F2, [1 shift]);
  F2_shifted(1:min(shift, numel(X))) = 0;
  F2_shifted(end+shift:end) = 0;
  product = F2_shifted.*F1;
  integral(offset_i) = sum(product)/numel(X)*(X(end)-X(1));
  if (mod(offset_i, 30)==0)
    area(X, product, 'facecolor', 'yellow');
    hold on
    plot(X, F1, 'b', X, F2_shifted, 'r', X, integral, 'k', [offset offset], [0 2], 'k:')
    hold off
    axis([-1.5 3 0 1.1])
    xlabel('t');
    legend('Area under f(t)g(t)', 'f(t)', 'g(t)', '(f*g)(t)');
    grid on
    drawnow
    
    set(gcf,'PaperPositionMode','auto')
    print('-dpng', '-r72', '-painters', sprintf('/tmp/conv_box_spike_%06d.png', offset_i));
    
  end
end