MATLAB: Plot a smooth envelope for oscillation curves

envelopeMATLABsmooth envelope

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.

Best Answer

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.

Related Solutions

MATLAB: Trouble with Envelope Functions

The problem is, you don't really want an envelope.

For example, here are a couple of fits that will produce an envelope.

slm_upper = slmengine(x,y,'env','sup','plot','on','knots',30);

slm_lower = slmengine(x,y,'env','inf','plot','on','knots',30);

Those are envelope fits, i.e., least upper bound and greatest lower bound functions.

But what you have drawn are functions that sort of look like that, but go where you want them to go, ignoring some of your data. So they skip some points that you consider outliers. You want maybe a function that can intelligently (defined by what you consider an outlier) exclude perhaps some 1 to 5% of the points as outliers.

The problem is, the eye is good at seeing a pattern that it likes. The computer, not so good. Computers do what they are programmed to do.

Perhaps the best suggestion I can offer is to use a tool like my SLM as below in a multiple step process:

slm_upper0 = slmengine(x,y,'env','sup','plot','on','knots',30);
tol= max(y)*1.e-14;
res_upper = slmeval(x,slm_upper,0) - y;
keep_upper = find(res_upper > tol);
drop_upper = find(res_upper <= tol);
slm_upper = slmengine(x(keep_upper),y(keep_upper),'env','sup','plot','on','knots',30);
hold on
plot(x(drop_upper),y(drop_upper),'ro')

Thus, find the points that were on the boundary in one envelope, then exclude them form the fit, and repeat the fit. Do a similar procedure for a lower semi-envelope. I'm not sure I see a better way.

The SLM toolbox is on the file exchange.

MATLAB: How to make a plot smooth

It sounds like you want a kind of interpolation, because "smoothing" usually trims the values of the extreme points of a curve, whereas interpolation fits those points exactly (as per your requirement that "the peak should be at same point").

Because I do not have your data here is a simple example using pchip.There are other 1D interpolation functions to choose from, so you should take a look and pick one that best suits your needs.

>> Y = [1,1,2,1,1];
>> X = [0,1,3,4,5];
>> Xi = 0:0.1:5;
>> Yi = pchip(X,Y,Xi);
>> plot(Xi,Yi,X,Y)

Best Answer

Related Solutions

MATLAB: Trouble with Envelope Functions

MATLAB: How to make a plot smooth

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