MATLAB: Cross-Correlation for noise reduction

corss-correlationdenoisingnoise reduction

Dear All,
I have two signals one is highly noisy (x1) and the other has less noise (x2) where the original signal x is the same. I want to denoise the signal (x2), and the fisrt method comes to my mind is using cross-correlation method, provided that I dont know the original function form and only have these two noisy sequences. However I am not sure how to do this. Accosring to my understanding, the cross correlation returns peaks where these signals are correlated as a fuction of lag and not return a denoised time domain signal. Can I use cross-correlation method to get third time-domain (which should be near or the same of x) signal let say x3 with less noise than x1 and x2?
Your omments are highly appreciated.
t=0:0.001:10;
x=sin(t);
x1=x+0.5*rand(size(x));
x2=x+0.1*rand(size(x));

Best Answer

Have you considered using a wiener filter (very simple with toolbox function) or BSS (blind source separation) or ICA (Independent Components Analysis) (both more complicated) to tease out your true signal?
ICA
ICA2
ICA3
Or consider using a lock-in amplifier to capture your signal without noise to begin with?
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