Create nonlinear trend via trapmf function (trapezoidal signal)

Hello there :)

I have created the following trend:

This is the script I have used to for that:

%%init
clear;              % clear workspace
close all;          % close all figures

%%defintions
Fs = 2;
Ts = 1/Fs;

t =0:Ts:30;

%%create trapezoidal signal
% time vectors for trapezoidal signal
t_1 = t(1,1:((3/Ts)));
t_2 = t(1,((3/Ts)+1):((16/Ts)));
t_3 = t(1,((16/Ts+1)):((19/Ts)));
t_4 = t(1,((19/Ts+1)):end);

% trapmf(time_vector,[Start_of_trapez, First_edge_ second_edge, end_point])
trapez_1 = trapmf(t_1,[.5 1 2 2.5]); 
trapez_2 = (trapmf(t_2,[3 3.5 4.5 5]))*-1;      % inverse trapezoidal signal
trapez_3 = (trapmf(t_3,[16.5 17 18 18.5]))*-1; 
trapez_4 = (trapmf(t_4,[19 19.5 20.5 21]));

% create complete signal containing trapez_1 to trapez_4
signal = [trapez_1 trapez_2 trapez_3 trapez_4];

%%plot signal
plot (t,signal);
xlabel('x');
ylabel('y');
title ('Nonlinearity');
grid on;

I would like to create a nonlinear trend for the marked areas on the picture above (I've only marked the first area for example). For this purpose, I would like to use a cubical function to create a nonlinear trend between the stationary areas. From my point of view, the way to do this is define a cubical function and add it to the areas, where a linear trend exists.

Is there any trick to do this with the created trapezoidal signal? I need to remain the rest of the signal as it is right now (that's what makes it tricky for me...)

I would be really thankful for any help :)

Thanks in advance.

Best regards, Niko

Answer 1

[Student88]

Hey there :)

I've solved my problem with Matlab function: interp1.

x1 = [0 0.125 0.25 0.375 0.5]; % define time points for cubical function
y1 = [0 0.4 0.6 0.65 1];       % define resulting y-data

xq1 = 0:0.001:0.5;                    % time points for first acceleration (upwards)
vq1 = interp1(x1,y1,xq1,'spline');    % resulting y-data for cubical function

plot(xq1,vq1);