Signal Decomposition for a mixed signal

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Coo Boo
Coo Boo 2019-12-18
评论： Srivatsa Dasa 2022-4-2
Hi friends,
Suppose we have a mixed signal X composed of three component signals x1, x2, and x3:
t=0:0.00001:0.3;
x1=(exp(-3*t)).*(0.2*sin(2*pi*400*t));
x2=1.2+(exp(-1.5*t)).*(1.1*sin(2*pi*40*t+pi/6));
x3=(exp(-5*t)).*(0.8*sin(2*pi*75*t+pi/3));
X=x1+x2+x3;
subplot(4,1,1);
plot(t,x1);title('Component signal: x1');
subplot(4,1,2);
plot(t,x2);title('Component signal: x2');
subplot(4,1,3);
plot(t,x3);title('Component signal: x3');
subplot(4,1,4);
plot(t,X);title('Mixed signal: X=x1+x2+x3');
Now, inversely, how can we obtain the samples of the three component signals x1, x2, and x3 without any additional information except the samples of the mixed signal X?
I would be very grateful if anyone could provide a code or efficient technique for this challenging example.
Thanks in advance for your help.
Note: Unfortunately, the ICA package and also the function emd() did not lead to a desired result. Is there any other practical solution for this example?
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Coo Boo
Coo Boo 2019-12-19
The idea came to my mind, but the filtering would also have some losses and frequency overlap, and I think the result might not be very good. Can you provide the code for investigating the result of this idea for this example?
Ridwan Alam
Ridwan Alam 2019-12-19
Posted below as an answer. Hope this helps!

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Ridwan Alam
Ridwan Alam 2019-12-19
t=0:0.00001:0.3;
x1=(exp(-3*t)).*(0.2*sin(2*pi*400*t));
x2=1.2+(exp(-1.5*t)).*(1.1*sin(2*pi*40*t+pi/6));
x3=(exp(-5*t)).*(0.8*sin(2*pi*75*t+pi/3));
X=x1+x2+x3;
untitled.png
fs = 1/.00001;
z1 = highpass(X,350,fs);
z3 = bandpass(X,[60 100],fs);
z2 = X - (z1 + z3);
Z = z1 + z2 + z3;
untitled1.png
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Ridwan Alam
Ridwan Alam 2019-12-23
编辑：Ridwan Alam 2019-12-23
Indeed. This answer assumes the pass bands are known beforehand. Moreover, the exponentially decaying function is not really decomposed well, as their frequency bands are different than the sin components. It just answers toy examples for learning filters, do not use in real general purpose applications.
Srivatsa Dasa
Srivatsa Dasa 2022-4-2
how to decompose a random .wav signal if its pass bands are unknown. Is it possible to decompose the signal

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