MATLAB: Trouble with Envelope Functions

envelope

Hi,

I have been trying to obtain a smooth envelope of my data. I have tried using other peoples solutions from the file exchange but unable to get a smooth envelope. See attached images.

Attached is the relevant data.

If anyone can recommend a file exchange or other solution would be much appreciated!

Thanks!

Best Answer

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.

Related Solutions

MATLAB: Plot a smooth envelope for oscillation curves

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.

MATLAB: How extracted envelop signal in matlab 2013

Use the hilbert function, specifically:

DbEnv = abs(hilbert(Db));

Example —

t = 0:0.01:5;                                                       % Create Data

s = sin(2*pi*t) .* cos(2*pi*10*t);                                  % Create Data
psenv = abs(hilbert(s));                                            % Upper Envelope
nsenv = abs(hilbert(-s));                                           % Lower Envelope
figure
plot(t, s, 'LineWidth',1.5)
hold on
plot(t,  psenv, '-r', 'LineWidth',2)
plot(t, -nsenv, '-g', 'LineWidth',2)
hold off
grid
legend('Signal','Upper Envelope','Lower Envelope', 'Location','N')

Best Answer

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MATLAB: How extracted envelop signal in matlab 2013

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