MATLAB: How to plot a restoration-based envelope in matlab

curve fittingenvelopeMATLABplotplotting

Hello greetings to everyone

I have a damping sine curve (code and data attached) as the following

and I intend to do the following action on it, and make an envelope like the dashed curve:

How can I plot these max and min and plot a fit envelope like the dashed curve as above in MATLAB (The crosses are the midpoint of each line on which they are located)

Thanks in advance for your time given on this question and stay healthy

Best Answer

Here's a "starter for ten"! I've used approximate time intervals:

T = t(end)/10;        % period - there seem to be 10 periods in the range
it = t(t<=T);         % times up to one period
dt = numel(it)/2;     % number of time points in a half period
n = 20;               % total number of half periods
mn = zeros(n,1);      % store for minima
mn(end) = min(R1);    % last minimum
mx = mn;              % store for maxima
mx(1) = 1;            % first maximum
% Find sizes of minima and maxima
for i = 2:n
    tspan = (i-1)*dt:i*dt;
    mn(i-1) = min(R1(tspan));
    mx(i) = max(R1(tspan)); 
end
% Assume "restoration" times occur at half period intervals
% starting at T/4 (an approximation)
Ravpts = (mn+mx)/2;
tavpts = (T/4:T/2:n*T/2);
% Interpolate for "restoration" plot
tav = T/4:t(end);
Rav = interp1(tavpts,Ravpts,tav,'pchip');
% Plots
plot(t,R1,tavpts,Ravpts,'o',tav,Rav,'k--'), grid
xlabel('t'),ylabel('damped sinusoid')
legend('data','restoration points','interpolated restoration')

This is the result: