Signal Decomposition for a mixed signal

22 次查看（过去 30 天）

显示更早的评论

Coo Boo 2019-12-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/497221-signal-decomposition-for-a-mixed-signal

评论： Srivatsa Dasa 2022-4-2

采纳的回答： Ridwan Alam

在 MATLAB Online 中打开

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 个评论
显示 3更早的评论隐藏 3更早的评论

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 2019-12-19

Posted below as an answer. Hope this helps!

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Ridwan Alam 2019-12-19

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/497221-signal-decomposition-for-a-mixed-signal#answer_407101

在 MATLAB Online 中打开

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 个评论
显示 1更早的评论隐藏 1更早的评论

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.