How to divide a data set into three different vectors based on peaks

Question

I have a large data set that, when graphed, resembles the graph of sin(x)+1 with three peaks. I want to integrate under each peak and get three different areas. I do not know the coordinate location of the peak, and I cannot assume that I know the wavelength. So I need to find the three peaks and separate the data into three corresponding vectors. Any help would be greatly appreciated.

Answer 1

You can accomplish what you want using the findpeaks function. Take the following example:

We generate two vectors x and y of data:

x = linspace(0, 5*pi);  % x data.
y = sin(x) + 1;         % y data.

Then we use findpeaks to find the peaks of our dataset and retrieve their indexes (locs):

>> [~, locs] = findpeaks(y)

locs =

    11    51    90

We can see that the function has found 3 peaks with coordinates: [x(11), y(11)], [x(51), y(51)] and [x(90), y(90)].

By calling findpeaks without output arguments we can get a plot of the data with the peak values overlaid which is often useful for a visual verification:

>> findpeaks(y)

We can divide our dataset very easily with the following for loop, and store the different subsets in a cell array:

n = numel(locs);
for i = 1:n + 1
    if i == 1
        x_cell{i} = x(1:locs(i));
        y_cell{i} = y(1:locs(i));
    elseif i <= n
        x_cell{i} = x(locs(i-1):locs(i));
        y_cell{i} = y(locs(i-1):locs(i));
    else
        x_cell{i} = x(locs(i-1):end);
        y_cell{i} = y(locs(i-1):end);
    end
end

This will give us:

K>> x_cell

x_cell =

  1×4 cell array

    [1×11 double]    [1×41 double]    [1×40 double]    [1×11 double]

and

K>> y_cell

y_cell =

  1×4 cell array

    [1×11 double]    [1×41 double]    [1×40 double]    [1×11 double]

So we have divided our dataset successfully. Each cell contains a subset of the original dataset.

Now we can use trapz inside a for loop to find the numerical integration of each subset:

k = numel(y_cell);
for i = 1:k
    A(i) = trapz(x_cell{i}, y_cell{i});
end

These are the results:

>> A

A =

    2.6004    6.4099    6.0931    2.6004

Finally I thought it would be nice to plot the different regions together using the area function and a for loop:

hold on;
for i = 1:k
    area(x_cell{i}, y_cell{i}, 'FaceColor', i/k*[1, 1, 1]);
end
hold off; axis tight;
grid on; box on;

The different regions are clearly visible here: