How to match the rising starting point of the graph

I want the graphs to have the same rising starting point.

Moving the graph by a certain value has a similar starting point.

However, it is very difficult and takes a long time to find the values one by one.

There is so much noise in the signal that I don't know how to code it.

I subtracted y(:,1) from the code to start from the origin.

[Walter Roberson]

First you need to decide how to distinguish an increase due to noise, as opposed to a "true" rise.

Is the noise independent? Is it proportional? Could you, for example, use a moving average (low pass) filter and then findpeaks with a minimum width?

[dpb]

Wonder if the findchangepts function might work? Just saw another Q? that looked like it did a great job in finding step change in a noisy signal...or looking into the preprocessing/filtering/smoothing it does.

[dpb]

Alternately, one might consider a piecewise regression of the section from beginning to the peak. I've posted this several times, the one I found first is at <Piecewise Regression>

[대수 김]

Thank you for the good advice.

I'll look it up and study it.

Answer 1

[Star Strider]

This is my best effort. I could not get the other functions I tried (ischange, findchangepts, islocalmin, etc.) to work, so I went with a somewhat less-sophisticated approach that finds the approximate indices of the threshold, then uses those values to correct for the x-offsets —

LD = load('ld.mat');
x = LD.signal.x;
y = LD.signal.y;

L = numel(x);
yf = sgolayfilt(y, 3, 1501);                                        % Filter Signal
Threshold = 0.000075;
for k = 1:size(y,2)
    zci(k) = find(diff(sign(yf(:,k)-Threshold)),1,"first")          % Index Of First Threshold-Crossing
end
Lmax = L-max(zci)-1000;                                             % Maximum Vector Length
Offset = 2500;                                                      % Set To 0 To Begin At Origin
for k = 1:size(y,2)
    idxrng = (zci(k) : zci(k)+Lmax)-Offset;                         % Index Range With Initial Offset
    yfc(:,k) = yf(idxrng,k);                                        % Filtered, Corrected
    yc(:,k) = y(idxrng,k);                                          % Original, Corrected
end

figure
plot(x(1:Lmax+1),yfc)
grid
title('Filtered, Shift-Corrected')
legend(compose('y_%d',1:size(y,2)), 'Location','best')

figure
plot(x, yf)
grid
title('Filtered, Uncorrected')
legend(compose('y_%d',1:size(y,2)), 'Location','best')

figure
plot(x(1:Lmax+1), yc)
grid
title('Original, Shift-Corrected')
legend(compose('y_%d',1:size(y,2)), 'Location','best')

The code produces three plots, the third being the most relevant —

.

[dpb]

Very, very nice, @Star Strider!!!

[Star Strider]

@dpb — Thank you!

[대수 김]

I'm late to thank you because I was studying while modifying the code you told me by myself.

Thanks to you, I get to know new functions and code structures.

Especially zci(k) = find(diff(sign(yf(:,k)-Threshold)),1,"first"); was very helpful.

Is there a reason why you usually use sgolayfilt among data filtering?

Have a nice day!

[Star Strider]

My pleasure!

I use sgoiayfilt to filter the data in order to remove most of the noise. Without the filtering, with the noise left in, the problem is essentially impossible to solve.

If my Answer helped you solve your problem, please Accept it!

.