From your description, I understand that you have a data vector and on the basis of number of points in that vector, you want to have a trapezoidal wave composed of rise, plateau and fall with plateau to last for a specific duration (ex 60 secs).
A = rand(1, 1000); % Example data vector A
total_points = length(A);
% Adjust below parameters
plateau_duration = 60;
total_duration = 180;
a = 0.5;
The number of points assigned to each segment is proportional to its duration. Since the total number of points is equal to the length of the data vector, the number of points for the plateau is calculated based on how long the plateau lasts compared to the total time.
Kindly follow the below code to generate a single pulse and extrapolate it to meet the requirements:
% Calculate points for each segment
plateau_points = floor(total_points * (plateau_duration / (total_duration)));
rise_fall_points = (total_points - plateau_points) / 2;
% Generate the trapezoidal wave
t_rise = linspace(-pi/2, pi/2, rise_fall_points);
t_fall = linspace(pi, 0, rise_fall_points);
rise = (a/pi) * (asin(sin(t_rise)) + pi/2);
plateau = a * ones(1, plateau_points);
fall = (a/pi) * (acos(cos(t_fall)) - 0);
% Concatenate segments
trapezoidal_wave = [rise, plateau, fall];
% Plot the trapezoidal wave
t = linspace(0, total_points, numel(trapezoidal_wave)); % Time vector
plot(t, trapezoidal_wave);
xlabel('Time');
ylabel('Amplitude');
title('Trapezoidal Wave Train');
grid on;
This method resembles the given equation and enables control over the plateau's duration and the overall length of the wave train by adjusting the data vector's length. The parameters can be tweaked to achieve the desired waveform.
I hope this points you in the right direction!
