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This question already has an answer here:

As shown in the figures, both of my signal and noise have the same frequency domain, how can I separate them?

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enter image description here

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marked as duplicate by MBaz, Matt L., A_A, Peter K. Dec 11 '16 at 15:53

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  • $\begingroup$ Sorry . I mistake the picture. The left picture is the noise and right picture is the signal . $\endgroup$ – LiuYang Nov 25 '16 at 8:27
  • $\begingroup$ I've edited to display the images. So, what's on top and bottom ? $\endgroup$ – Gilles Nov 25 '16 at 8:38
  • $\begingroup$ Answer upvotes and better answer validation are required for this question $\endgroup$ – Laurent Duval Jul 28 at 14:46
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As you have noticed, it is quite unlikely that you can filter your data with a standard frequency filter, thus a linear filter.

Unless the signal and the noise are well separated in time, unless you have a model, you will probably need to resort to other techniques, such as nonlinear filtering, time-frequency or time-scale filtering, or add additional information or assumptions, such as thought signal or noise properties (to name a few: gaussianity, positivity, independence, sparsity), and bend to blind source separation, latent variable analysis, nonlinear matrix separation, etc.

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