Divide and plot signal parts
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Mathieu NOE on 23 Aug 2022
Edited: Mathieu NOE on 23 Aug 2022
finally, decided to give it a try ....
your neg data in red (added for fun the positive segments as well in green)
%% dummy data
fs = 100;
samples = 6.5*fs;
dt = 1/fs;
t = (0:samples-1)*dt;
x = square(2*pi*0.5*t);
% high pass filter
fc = 0.25;
wn = 2*fc/fs;
[b,a] = butter(1,wn,'high');
xf = filter(b,a,x);
% apply a slope / shift
xf = xf + 3*(-1 + t./max(t));
%% main code
% first and second derivatives
[dxf, ddxf] = firstsecondderivatives(t,xf);
% start / stop points for negative data
all_points = find(ddxf>max(ddxf)/10); % adjust threshold according to your data
dd = diff(all_points);
ind_neg = find(dd<mean(dd));
start_point_neg = all_points(ind_neg);
stop_point_neg = all_points(ind_neg+1);
ll_neg = stop_point_neg - start_point_neg;
% start / stop points for positive data
ind_pos = find(dd>mean(dd));
start_point_pos = all_points(ind_pos)+1;
stop_point_pos = all_points(ind_pos+1)-1;
ll_pos = stop_point_pos - start_point_pos;
for ci = 1:numel(ll_neg)
id_neg = start_point_neg(ci):stop_point_neg(ci);
for ci = 1:numel(ll_pos)
id_pos = start_point_pos(ci):stop_point_pos(ci);
function [dy, ddy] = firstsecondderivatives(x,y)
% The function calculates the first & second derivative of a function that is given by a set
% of points. The first derivatives at the first and last points are calculated by
% the 3 point forward and 3 point backward finite difference scheme respectively.
% The first derivatives at all the other points are calculated by the 2 point
% central approach.
% The second derivatives at the first and last points are calculated by
% the 4 point forward and 4 point backward finite difference scheme respectively.
% The second derivatives at all the other points are calculated by the 3 point
% central approach.
n = length (x);
dy = zeros;
ddy = zeros;
% Input variables:
% x: vector with the x the data points.
% y: vector with the f(x) data points.
% Output variable:
% dy: Vector with first derivative at each point.
% ddy: Vector with second derivative at each point.
dy(1) = (-3*y(1) + 4*y(2) - y(3)) / (2*(x(2) - x(1))); % First derivative
ddy(1) = (2*y(1) - 5*y(2) + 4*y(3) - y(4)) / (x(2) - x(1))^2; % Second derivative
for i = 2:n-1
dy(i) = (y(i+1) - y(i-1)) / (x(i+1) - x(i-1));
ddy(i) = (y(i-1) - 2*y(i) + y(i+1)) / (x(i-1) - x(i))^2;
dy(n) = (y(n-2) - 4*y(n-1) + 3*y(n)) / (2*(x(n) - x(n-1)));
ddy(n) = (-y(n-3) + 4*y(n-2) - 5*y(n-1) + 2*y(n)) / (x(n) - x(n-1))^2;