Signal Separation from a Mixed Signal

Question

Sohel Rana 2020-12-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/689894-signal-separation-from-a-mixed-signal

评论： Sohel Rana 2020-12-10

Hi,

I have signal that is consists of three individual signals. How can I separate these individual signals from the mixed signal. Figure 1 (upper one) shows the mixed signal spectrum and lower one shows the FFT of that signal. It is clear that there are three peaks due to the three signals. The figure 2 shows the I_first and I_second signals which was computed from the FFT figure (figure 1). The figure 2 I got from a paper. How can I obtain such figure 2 from the figure 1? Ignore the unit of the axis. Any help would be appreciated.

m=1000; I1=0.5; I2=0.3; I3=0.2; L1=73*m; L2=140*m; n1=1; n2=1.444;

lam=m*(1.52:0.000001:1.58);

Q12=(4*pi*n1*L1)./lam; Q23=(4*pi*n2*L2)./lam; Q13=Q12+Q23;

figure(1)

I_first=I1+I2+2*sqrt(I1*I2).*cos(Q12); % first signal

I_second=I2+I3+2*sqrt(I2*I3).*cos(Q23); % second signal

I_third=I1+I3+2*sqrt(I1*I3).*cos(Q13); % third signal

I=2*(I1+I2+I3)+2*sqrt(I1*I2).*cos(Q12)+2*sqrt(I2*I3).*cos(Q23)+2*sqrt(I1*I3).*cos(Q13); % mixed/combined signal

subplot(2,1,1)

plot(lam,I)

%%FFT

L = numel(lam);

Ts = mean(diff(lam));

Fs = 1/Ts;

Fn = Fs/2;

FTI = fft(I)/L;

Fv = linspace(0, 1, fix(L/2)+1)*Fn;

Iv = 1:numel (Fv);

[pks,locs] = findpeaks(abs(FTI(Iv)));

subplot(2,1,2)

plot(Fv, abs(FTI(Iv)));

xlim([0 0.5]);

xlabel('Spatial Frequency (nm^{-1})')

ylabel('Amplitude')

text(Fv(locs), abs(FTI(locs)), sprintfc('Peak%d',(1:numel(locs))), 'HorizontalAlignment','center', 'VerticalAlignment','bottom')

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Answer 1

Image Analyst 2020-12-10

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https://ww2.mathworks.cn/matlabcentral/answers/689894-signal-separation-from-a-mixed-signal#answer_571504

If you know the frequency ranges of each component signal, then simply create a bandpass filter by taking the complete spectrum and zeroing out the parts that are outside the range of each signal. Now you have 3 FFTs, each one with only one signal in it. Then IFFT those to get back to the original 3 time domain component signals.

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Sohel Rana 2020-12-10

Thank you so much. What I know about the signals I mentioned in the code. How could I know the range of frequency of each component? I can find the center frequency of each signal from the FFT. How can I zeroing out the parts that are outside the range of each signal? Could you please help me to resolve the problem?

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