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# How to create an envelop from three graphs

Asked by Lisa Justin on 3 Sep 2012

How can i create an envelop for three different Signals. the edges around the three signals that are top most, so there is an envelop around all three but forming 1 plot around all three. All three signals are plotted on the same graph

## 1 Comment

Jan Simon on 3 Sep 2012

It would be helpful, if you post any details. Do you have the "graphs" on paper, as picture file, as FIG file, as data of a text file, as MAT file or available as arrays? Do the grpahs share the same X-values or do you have to interpolate at first?

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Answer by Jan Simon on 3 Sep 2012

For the most trivial case, when the three lines share the same X-values and are provides as vectors:

```x = 1:100;
y1 = rand(1, 100);
y2 = rand(1, 100);
y3 = rand(1, 100);
joined  = cat(1, y1, y2, y3);
env_max = max(joined, [], 1);
env_min = min(joined, [], 1);
```
```plot(x, joined);
hold('on');
plot(x, env_max, 'k');
plot(x, env_min, 'k');
```

Jan Simon on 4 Sep 2012

If a curve is a tangent to three other lines, these lines must be identical in each point, because they have the same slope and the same position. Please choose any more appropriate explanation of the result you are trying to achieve. Please, Lisa, do not let us guess the details, because this wastes your and our time. Thanks.

Lisa Justin on 5 Sep 2012

I will try to post a plot so it is easy to understand what i mean

Elige Grant on 5 Sep 2012

I generally use hilbert to give me the analytic signal, which I then take the abs to give me my envelope of a single signal. If this is what you are after, then maybe this will work (expanding on Jan's answer):

```>> hilb = max(abs(hilbert(joined)),[],1);
>> plot(f,joined,f,hilb)
```

Or maybe you need to perform the Hilbert transform on the distance your individual data-point is from the origin (0,0,0) i.e.,

```sqrt(y1.^2+y2.^2+y3.^2)
```

So...

```>> hilb2 = max(abs(hilbert(sqrt(y1.^2+y2.^2+y3.^2))),[],1)
>> plot(f,joined,f,hilb2)
```