Signal Decomposition for a mixed signal
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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?
5 commentaires
Réponse acceptée
Ridwan Alam
le 19 Déc 2019
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;
fs = 1/.00001;
z1 = highpass(X,350,fs);
z3 = bandpass(X,[60 100],fs);
z2 = X - (z1 + z3);
Z = z1 + z2 + z3;
3 commentaires
Ridwan Alam
le 23 Déc 2019
Modifié(e) : Ridwan Alam
le 23 Déc 2019
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
le 2 Avr 2022
how to decompose a random .wav signal if its pass bands are unknown. Is it possible to decompose the signal
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