plot a smooth envelope for oscillation curves

Hello, everyone, I would like to plot a smooth envelope for a oscillation curve. It seems that the function 'envelope' in MATLAB can be used to plot a envelope curve. But I cannot obtain a smooth envelope based on this function. Would anyone help me about this envelope curve? Following is the source data. Thanks.

[up,dw]=envelope(y,100,'analytic'); figure,plot(x,[up;dw])

[up,dw]=envelope(y,100,'peak'); figure,plot(x,[y;up;dw])

This is the kind of smooth envelope curve I want to obtain.

Answer 1

[Greg Dionne]

Do you have a particular selection criteria for the peaks or formula for how you would like the smoothing performed at the extremities?

I ran a spectrogram on your signal to see if there was a simple envelope to extract. It appears that there is, so maybe you could try to extract the amplitude ridges. (It seems a little bit of aliasing is in your sampled signal as well. Not sure if it's important, but have a look)

spectrogram(y,kaiser(256,40),250,[],1/mean(diff(x)),'power','yaxis')

I tried to extract a few ridges:

[sst,f] = fsst(y,1/mean(diff(x)),kaiser(256,10));
fridge = tfridge(sst,f,10,'NumRidges',6);
plot(x,fridge)

I got a reasonable hit on the fundamental, so perhaps you could attempt to extract the spectrum amplitudes along those frequencies to get a good sense of the power envelope.

[ZhiH]

Thanks a lot! It is really helpful.

Answer 2

[ZhiH]

Using the powerful tool, Shape Language Modeling, proposed by John D'Errico, I still cannot obtain a smooth envelope curve.

 [up,up_x,up_y] = slmengine(x,y,'env','sup','plot','off','knots',60); 
 [dw,dw_x,dw_y] = slmengine(x,y,'env','inf','plot','off','knots',50);
 figure, plot(x,[y;up_y;dw_y]);

[ZhiH]

Shape Language Modeling can be found at https://ww2.mathworks.cn/matlabcentral/fileexchange/24443-slm-shape-language-modeling