why envelope by hilbert increasing in tail of signal?

I have decay sinusiodal signal that I want to fit in, I use hilbert

% Extract the ACF data
% Calculate the starting and ending indices dynamically
half_length = floor(length(data) / 2); % Second half starts here
portion_len = floor(0.1 * half_length); % 10% of the second half
% Extract the 10% of the earlier data in the second half
y_obs = data(half_length:(half_length + portion_len - 1))';
y_obs_square= y_obs.^2;
t = 1:length(y_obs);
% Compute the squared envelope of the ACF 
envelope = abs(hilbert(y_obs_square));

but what I don't understand is why envelope giving increasing aplitude in the tail of signal as figure below?

can someone explain? Thanks in advance

Answer 1

[Mathieu NOE]

hello again

here 3 suggestions appart from the traditionnal hilbert transform

see the 2 functions in attachment

t = 0:0.001:2;
x = cos(2*pi*10*t).*exp(-5*t);

% obtain the envelope data
%--------------------------------------------
[up1,down1] = envelope(abs(x),07,'peak'); % option 1 with regular (TMW) envelope function
[up2,down2] = envelope2(t,abs(x),'linear'); % option 2 with envelope2 (see function attached)
[env] = env_secant(t, abs(x), 50, 'top'); % option 3 with env_secant (see function attached)
tf = islocalmax(x,'MinProminence',1e-4,'MinSeparation',5); % option 3 with islocalmax (you can also try with find peaks)
tt = t(tf);
xt = x(tf);
plot(t,x,t,up1,t,up2,tt,xt,t,env)
legend('signal','envelope','envelope2','islocalmax','env secant');

[nirwana]

thanks @Mathieu NOE for providing the envelope function. but what suggest by book that I've read is using hilbert, (while your function is trying to get envelope by connecting peak of input signal, CMIIW).

[Mathieu NOE]

yes you can use hilbert transform for signal envelope but it's not the sole and only way to do it.

and I prefer sometimes other alternatives because the result with hilbert does not please me.

[Mathieu NOE]

this may interest you :

filters - Envelope detection using matlab hilbert function - Signal Processing Stack Exchange

matlab - Envelope detection using hilbert transform - Signal Processing Stack Exchange

The envelope function was introduced in R2015b. It makes these problems easier.