Divide time series into regions

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Manolis Michailidis 2015-10-1

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评论： Manolis Michailidis 2017-11-6

Hello, i have a graph with rapidly changes and i need to divide it into regions like are shown in the picture

I can divide it considered the amplitude of each regions but that's not so appropreate because i have also big dicreases like in region B that reaches the previous region, and that's something that troubles me. I thought maybe i could use standard deviation between local peaks and local minima. What are youur thoughts and do you know any other simple (or not so) methods ? Thanks in advance. Note that this graph sould be divided unsmoothed , and then only each region will be processed.

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Answer 1

Star Strider 2015-10-1

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I don’t have your data so I can only describe an approach. I would use a low-pass filter with a very low frequency passband to isolate the d-c offset for each section. (Ideally, you should get a series of ‘steps’ as the output.) Then use those values to define the different regions. You will probably have to devise a way to deal with the transitions between the steps to define them correctly.

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Star Strider 2015-10-1

在 MATLAB Online 中打开

Was working on it. This is not a trivial problem!

My idea essentially worked:

D = load('Manolis Michailidis fo.mat');
fo = D.fo;
x = 0:length(fo)-1;
figure(1)
plot(x, fo)
grid
Ts = 1;                                         % Sampling Time Interval
Fs = 1/Ts;                                      % Sampling Frequency
Fn = Fs/2;                                      % Nyquist Frequency
Ffo = fft(fo)/length(fo);                       % Fourier Transform
Fv = linspace(0, 1, fix(length(Ffo)/2)+1)*Fn;   % Frequency Vector
Iv = 1:length(Fv);                              % Index Vector
figure(2)
plot(Fv, abs(Ffo(Iv)))
grid
axis([0  0.01    ylim])
Wp = 0.005/Fn;                                  % Normalised Passband Frequency
Ws = Wp/0.8;                                    % Normalised Stopband Frequency
Rp =  1;                                        % Passband Ripple
Rs = 10;                                        % Stopband Ripple
[n,Ws] = cheb2ord(Wp, Ws, Rp, Rs);              % Design Chebyshev Type II LPF
[b,a]  = cheby2(n,Rs,Ws,'low');
[sos,g] = tf2sos(b,a);                          % Use ‘SOS’ For Stability
fof = filtfilt(sos,g,fo);                       % Filter Signal
xidx = find((fof >= 2900) & (fof <= 3100));     % Interpolate To Find ‘x’ For ‘fo=3000’
xbrk = [find(diff([0 xidx]) > 100) length(xidx)];
for k1 = 1:length(xbrk)-1
    idxrng = xidx(xbrk(k1):xbrk(k1+1)-1);
    xt = interp1(fof(idxrng), x(idxrng), 3000, 'linear','extrap');
    segx(k1) = find(x <= xt, 1, 'first') + idxrng(1)-1;
end
figure(3)
plot(x, fo)
hold on
plot(segx, 3000*ones(length(segx)), '+r', 'MarkerSize',15)
hold off
grid

The ‘segx’ vector are the x-index ‘breakpoints’ in your data, based on using an ‘fo’ value of 3000 to distinguish the segments. Using the low-pass-filtered signal made defining the segments much easier.

It might be possible to make this more efficient, but I opted to leave the analysis section of the code in it, since not all of your data may have the same characteristics.

I finished this before I saw your uploaded time vector, so replace the ‘x’ vector in my code with your time vector. The ‘Ts’ assignment then becomes:

Ts = mean(diff(t));

where ‘t’ is your time vector. You will have to define the numerator in the ‘Wp’ assignment to correspond to the correct frequency derived from your time vector, but the code should otherwise work.

Manolis Michailidis 2015-10-1

it's all fine , thanks again

Star Strider 2015-10-1

O.K.

My pleasure.

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Answer 2

Ashim 2017-11-4

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You can also use alternatively the findchangepts() command from Matlab to find the different regions> here again, there are multiple options based on std dev or mean, or rms, or threshold. Try it out