Find the width of a peak

I have a csv data of an impact collected. I would like to measure the duration/width of the main peak.

The deepest peak is the main, but then there may be other peaks prior and another peak beginning before reaching the base.

As I am dealing with multiple peaks, how do I measure the width of just the beginning of deepest peak to its end?

The first image below is the graph of the impact. Second image zooms into the second peak beginning before reaching zero and the width i would like to find. Also attaching the raw csv data for reference.

Thanks a lot!

Answer 1

[Star Strider]

Try something like this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1053640/j1%20a30.csv', 'VariableNamingRule','preserve')

T1 = 5953×9 table
      __time      /leptrino_force_torque/force_torque/header/seq    /leptrino_force_torque/force_torque/header/stamp    /leptrino_force_torque/force_torque/wrench/force/x    /leptrino_force_torque/force_torque/wrench/force/y    /leptrino_force_torque/force_torque/wrench/force/z    /leptrino_force_torque/force_torque/wrench/torque/x    /leptrino_force_torque/force_torque/wrench/torque/y    /leptrino_force_torque/force_torque/wrench/torque/z
    __________    ______________________________________________    ________________________________________________    __________________________________________________    __________________________________________________    __________________________________________________    ___________________________________________________    ___________________________________________________    ___________________________________________________

    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                    2.9                                                  0.066                                                   -0.03                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                  2.925                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                  2.925                                                  0.066                                                 -0.0294                                                 0.102                       
    1.6568e+09                      1.9251e+06                                         1.6568e+09                                             0.475                                                  3.7                                                  2.925                                                  0.066                                                 -0.0294                                                 0.102                       

VN = T1.Properties.VariableNames.';
t = T1{:,1};
f = T1{:,[4 5 6]};

x = t;
y = f(:,3);

[pks,plocs] = findpeaks(-y, 'MinPeakProminence',20);                % Desired Peak & Index
[vys,vlocs] = findpeaks(y, 'MinPeakProminence',0.1);                % Valleys & Indices

[vlc,ixv] = mink(abs(vlocs-plocs),2);                               % Choose Two Closest Valleys To Desired Peak
vlcs = plocs + [1; -1].*vlc;                                        % Calculate Indices  

idxr = vlcs(2) : vlcs(1);                                           % Initial Index Range

figure
plot(x(idxr), y(idxr))                                              % Plot Desired Peak Region
hold on
plot(t(vlcs), y(vlcs), '^r')
hold off
grid
title('Isolated')

figure
plot(t, y)
hold on
plot(t(vlcs), y(vlcs), '^r')
hold off
grid
title('In Context')
xlim([-1 1]*1E-1 + t(plocs))
text(t(plocs), -5, sprintf('\\leftarrow %.6f \\rightarrow', diff(t(vlcs))), 'Horiz','center', 'Vert','middle', 'FontSize',8)

This uses code I recently wrote to define the valleys around a peak rather than the reverse, as required here. I changed it slightly for this problem.

.

[Samridh Jain]

This is amazing! Even better than I wanted, thank you so much! The plots would make it easier for me to derive the area under the graph as well.

[Star Strider]

As always, my pleasure!

To calculatee the area:

AUC = trapz(x(idxr), y(idxr))

NOTE — This will calculate the area with respect to y=0, so it may be necessary to correct the baseline to consistently be 0, depending on what you want.

Comparing the areas with the uncorrected and corrected baselilnes —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1053640/j1%20a30.csv', 'VariableNamingRule','preserve');
VN = T1.Properties.VariableNames.';
t = T1{:,1};
f = T1{:,[4 5 6]};

x = t;
y = f(:,3);

[pks,plocs] = findpeaks(-y, 'MinPeakProminence',20);                % Desired Peak & Index
[vys,vlocs] = findpeaks(y, 'MinPeakProminence',0.1);                % Valleys & Indices

[vlc,ixv] = mink(abs(vlocs-plocs),2);                               % Choose Two Closest Valleys To Desired Peak
vlcs = plocs + [1; -1].*vlc;                                        % Calculate Indices  

idxr = vlcs(2) : vlcs(1);                                           % Initial Index Range

B = [x(vlcs([2 1])) ones(2,1)] \ y(vlcs([2 1]));                    % Linear Regression Of Line Connecting 'vlcs' Points

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.154011e-20.

Baseline = [x(idxr) ones(size(x(idxr)))] * B;

figure
plot(x(idxr), y(idxr)-Baseline)                                     % Plot Desired Peak Region
hold on
plot(x(vlcs), y(vlcs)-Baseline([end 1]), '^r')
hold off
grid
title('Isolated, Baseline-Corrected')

AUC = trapz(x(idxr), y(idxr))                                       % Calculate Baseline-Uncorrected Area

AUC = -1.1678

AUC_BC = trapz(x(idxr), y(idxr)-Baseline)                           % Calculate Baseline-Corrected Area

AUC_BC = -1.0910

text(x(plocs), -10, sprintf('Baseline-Corrected AUC = %.6f',AUC_BC), 'Horiz','center', 'Vert','middle')

This is likely more accurate than simply using trapz on the uncorrected values, however that depends on how you want to calculate it.

.

[Samridh Jain]

Sorry to bother further...how would I be able to measure the width if it's a max peak? Above file deals with negative values, but after finding the resultant force, the values become positive. Attaching the MATLAB file for reference. I find the resultant of x,y,z so all values become positive.

[Star Strider]

No worries!

The positive peak code would work similarly. See: How can I get the mean data from under the graphs?

This was the original approach that I wrote this code for. I adapted it for the negative version with your data. The area code is similar as well, although it would likely need to be adapted to work with your data, similar to what I did with the negative peak areas.

EDIT — (3 Jul 2022 at 17:58)

For a specific peak, the code would be something like this —

x = (920 : 980).';                                              % Create Data (Column)
y = sinc((x-mean(x))/5);                                        % Create Data (Column)

figure
plot(x, y)
grid

[pks,plocs] = findpeaks(y, 'MinPeakProminence',1);              % Desired Peak & Index
[vys,vlocs] = findpeaks(-y, 'MinPeakProminence',0.1);           % Valleys & Indices

[vlc,ixv] = mink(abs(vlocs-plocs),2);                           % Choose Two Closest Valleys To Desired Peak
vlcs = plocs + [-1; 1].*vlc;                                    % Calculate Indices  

idxr = vlcs(1) : vlcs(2);                                       % Initial Index Range

hold on
plot(x(idxr([1 end])), y(idxr([1 end])), 'vr')
hold off

figure
plot(x(idxr), y(idxr))                                          % Plot Desired Peak Region
hold on
plot(x(idxr([1 end])), y(idxr([1 end])), 'vr')
hold off
grid

The area calculation would be similar to the negative peak code.

.

Answer 2

[Jonas]

do you just want to measure the peak width of this data set only? if yes, i should be telatively easy locating the peak with min() and the locating start and end of it by using e.g. islocalmax() to find last peak before main peak and first peak after main peak