Many measurements involve data collected asynchronously by multiple sensors. If you want to integrate the signals, you have to synchronize them. The Signal Processing Toolbox™ has functions that let you do just that.
For example, consider a car crossing a bridge. The vibrations it produces are measured by three identical sensors located at different spots. The signals have different arrival times.
Load the signals into the MATLAB® workspace and plot them.
load relatedsig ax(1) = subplot(3,1,1); plot(s1) ylabel('s_1') ax(2) = subplot(3,1,2); plot(s2) ylabel('s_2') ax(3) = subplot(3,1,3); plot(s3) ylabel('s_3') xlabel('Samples') linkaxes(ax,'x')
s2 and in turn leads
s3. The delays can be computed exactly using
finddelay. You see that
s1 by 350 samples,
s1 by 150 samples, and
s3 by 500 samples.
t21 = finddelay(s2,s1) t31 = finddelay(s3,s1) t32 = finddelay(s2,s3)
t21 = 350 t31 = -150 t32 = 500
Line up the signals by leaving the earlier signal untouched and clipping the delays out of the other vectors. Add 1 to the lag differences to account for the one-based indexing used by MATLAB®. This method aligns the signals using as reference the earliest arrival time, that of
axes(ax(1)) plot(s1(t21+1:end)) axes(ax(2)) plot(s2) axes(ax(3)) plot(s3(t32+1:end))
alignsignals to align the signals. The function works by delaying earlier signals, so use as reference the latest arrival time, that of
[x1,x3] = alignsignals(s1,s3); x2 = alignsignals(s2,s3); axes(ax(1)) plot(x1) axes(ax(2)) plot(x2) axes(ax(3)) plot(x3)
The signals are now synchronized and ready for further processing.