Hello
this is a code that will do the time shifting and sigma computation for a time shift of - 10 to + 10 samples
seems the two signals are pretty well time aligned as the error is minimal for a delta of 0 sample
now we could refine the analysis if we would resample the data with a smaller time increment.
you can uncommet those lines if you want to see the effect of time shift on the data - but this is not a key point here
% figure(1)
% plot(tra2,Pt2,tra2,Pra2)
% pause(1)
full code :
clc
clearvars
%% load('');
load('dataP.mat')
dt = mean(diff(t));
a = 2;
Pra = Pr/a; % normalize Pr data by factor a
%% main code
samples = 10;
delta_samples = (-samples:samples);
delta_t = delta_samples*dt;
for ci = 1:numel(delta_samples)
tra = t+delta_t(ci);
% find common time axis
ind = (tra>=min(t) & tra<=max(t));
tra2 = tra(ind);
Pra2 = Pra(ind);
% resample Pt data on time axis of Pra2 data (tra2)
Pt2 = interp1(t,Pt,tra2,'linear');
% figure(1)
% plot(tra2,Pt2,tra2,Pra2)
% pause(1)
% error (cf equation)
num = mean((Pt2(:)-Pra2(:)).^2);
den = mean((Pt2(:)).^2);
sigma(ci) = num./den;
end
figure(2)
plot(delta_t,sigma);
xlabel('Delta Time (s)');
ylabel('Sigma error');
title('Synchronization Error using Signal Time Shifting');
