How to create an envelop from three graphs

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

[Jan]

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?

Answer 1

[Jan]

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');

[Lisa Justin]

Thanks but i like to create an envelop along the edges of all three plots forming another plot

 y1 = rand(1, 100);
 y2 = rand(1, 100);
 y3 = rand(1, 100);
x=fft(y1);
y=fft(y2);
z=fft(y3);
joined  = cat(1, y1, y2, y3);
f = 1:100;
plot(f,joined)
hold on
plot(f, envelop) Not sure how to get this

 ?????
I need an envelop (max only) along all three plots so i can get a new plot showing the relevent parts,  i am using an accelerometer with three directions x,y,z. With LMS test Lab an envelop could by created  but i need to do the same with Matlab, but i do not know how to.

[Jan]

What's wrong with:

env_max = max(joined, [], 1);
plot(x, env_max, 'k');

?? Please define mathematically, what you call "envelope".

[Lisa Justin]

The new curve (envelope) should be tangent on all three curves.

[Jan]

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]

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

[Dr. Seis]

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)

Does that look about right?

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)