How can I align deterministic signals?

I have some results from a shaking table test that have been carried out.

The input was always the same, however, records where started "by-hand" so they always have different starting times leading to signals that are not aligned. Since I am not an expert in signal processing, I need some help to align them.

I add some example data to this topic to give an idea about the data.

Answer 1

[Star Strider]

Probably the easiest way to do this (with these signals) is simply to threshold the beginning of each to get the index, then use that to adjust the start times for each signal to the same offset.

Try this —

files = dir('*.mat');

for k = 1:numel(files)
    LD = load(files(k).name);
    fn = fieldnames(LD);
    s(k,:) = struct2cell(load(files(k).name, fn{:}));
    L(k) = length(s{k});
    Fs = 1;
    t{k,:} = linspace(0, L(k)-1, L(k))/Fs;
end


figure
hold on
for k = 1:numel(files)
    plot(t{k}, s{k})
    % ylim([-1 1])
    start(k) = find(s{k} > 0.05,1);
end
hold off
grid

[earliest,eidx] = min(start)

earliest = 8221

eidx = 3

figure
tiledlayout(numel(files),1)
for k = 1:numel(files)
    nexttile
    plot(t{k}, s{k})
    grid
    xlim([0.75 1.5]*1E+4)
end
sgtitle('Original Signals')

figure
tiledlayout(numel(files),1)
for k = 1:numel(files)
    idxrng = start(k) : numel(s{k});
    ta{k} = t{k}(1:numel(idxrng));                          % Adjusted Time Vector
    sa{k} = s{k}(idxrng);                                   % Adjusted Signal Vector
    nexttile
    plot(ta{k}, sa{k})
    grid
end
sgtitle('Time-Adjusted Signals')

.

[alegio20]

Thank you very much!

[Star Strider]

As always, my pleasure!

Answer 2

[Peter Perkins]

Some of what SS shows might be easier with timetables:

for i = 1:4
    signal = load("ew_data"+i+".mat"); signal = signal.ans;
    start = find(abs(signal)>0.05,1,'first');
    stop = find(abs(signal)>0.05,1,'last');
    tt{i} = timetable(signal(start:stop),RowTimes=seconds(1:(stop-start+1))); % dunno what your time units are
end
ttAll = synchronize(tt{:},"union");
ttAll.Properties.VariableNames = "Signal" + (1:4);
stackedplot(ttAll)

[Image Analyst]

+1 vote for letting us know about synchronize

[Peter Perkins]

Huh. I think of synchronize as "the value proposition" for timetables. Are you saying you did not know about it? If true, that suggests a documentation shortcoming that we will have to identify.

[Star Strider]

I’ve used synchronize and like it. The problem here is that the time vectors weren’t provided (I had to synthesise them in my response), so without even a sampling frequency (that I arbitrarily assumed was the same for all signals), it didn’t seem applicable.

[Peter Perkins]

Right. I made a lot of assumptions about the time vectors.

[alegio20]

@Star Strider your assumption was correct, and the sampling frequency was the same for every signal: 200 Hz.

[alegio20]

Thanks for all the great suggestion provided! I will indeed try to use synchronize soon!