MATLAB: Superposition of all graphs

alignmentsuperposition of waves

I'm trying to find the overall effect of power production across each graph. Basically the graphs produced from the following code need to be added together, but as you can see there is phase shift, so as you see the graphs when running the code, that's exactly how they need adding. You will notice there is phase shift and this needs to remain where it is. I want to add all of the y-values together essentially and put them onto one graph, taking into perspective that there is phase shift in the sites. The X-range needs to remain at [0 29.53]. I've attached the Excel file that's imported. Thanks for looking into this 🙂
[data, titles, r]=xlsread('Tidal Sites.xlsx');
A=data(:,7);
B=data(:,10);
C=data(:,11);
D=data(:,12);
E=data(:,6);
F=titles(:,2);
G=data(:,14);
for k=1:length(E)
      if ~isnan(E(k))
          x1=linspace(0, 7.3826475, 10000);
          y1=(abs(det(A(k))*((exp(1).^(det(-B(k)).*x1))).*cos((det(C(k)).*x1))));
          figure, plot(x1 + E(k)/24 ,y1), hold on
x2 = x1(end) + cumsum(fliplr(diff(x1))); 
y2 = fliplr(y1(1:end-1)); %Reflection after the first quarter of lunar cycle
x3 = x2(end) + cumsum(fliplr(diff(x2)));
y3 = fliplr(y2(1:end-1)); 
x4 = x3(end) + cumsum(fliplr(diff(x3)));
y4 = fliplr(y3(1:end-1)); %2 more reflections to give lunar cycle
x5 = x4(end) + cumsum(fliplr(diff(x4)));
y5 = fliplr(y4(1:end-1)); % an additional quarter of cycle to make up for phase difference FORWARD
x6 = -cumsum(fliplr(diff(x1)));
y6 = y1(1:end-1); %an additional quarter of cycle to make up for phase difference BEHIND
   x = horzcat(flip(x6), x1, x2, x3, x4, NaN, x5, NaN);
   y = horzcat(flip(y6), y1, y2, y3, y4, NaN, y5, NaN);
plot(x + (E(k)/24), y), hold on 
   title(F(k+1))
           xlabel('Time (days)')
           ylabel('Power (GW)')
           xlim([0 29.53]);
      end
end

Best Answer

I didn't dig into this uncommented alphabet soup of a program, but you can align waveforms if you use normalized cross correlation, or normxcorr2() in the Image Processing Toolbox.
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