why envelope by hilbert increasing in tail of signal?

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nirwana 2024-12-16

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评论： Mathieu NOE 2024-12-16

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

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Answer 1

Mathieu NOE 2024-12-16

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在 MATLAB Online 中打开

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');